%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP108^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:43 AM UTC 2026
% Result : Theorem 16.57s 2.78s
% Output : Refutation 16.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP108^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:55:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.99/0.95 % (3651806)Will run a generic schedule for satisfiability detection.
% 3.99/0.95 % (3651811)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=867969335_2999 on theBenchmark for (2999ds/0Mi)
% 3.99/0.95 % (3651812)% WARNING: option uhcvi not known.
% 3.99/0.95 % (3651812)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1004681374:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.99/0.95 % (3651816)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=120696199:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.99/0.95 % (3651813)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2310401975:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.99/0.95 % (3651814)dis+10_1_sil=32000:sp=arity:random_seed=3653275102:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.99/0.95 % (3651815)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2497684531:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.99/0.95 % (3651817)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=122137244:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.99/0.95 % Exception at run slice level
% 3.99/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.99/0.95 % (3651812)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.99/0.95 % (3651815)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.99/0.95 % (3651825)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3088693305:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.99/0.95 % (3651814)Instruction limit reached!
% 3.99/0.95 % (3651814)------------------------------
% 3.99/0.95 % (3651814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.99/0.95 % (3651814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/0.95 % (3651814)CaDiCaL version: 2.1.3
% 3.99/0.95 % (3651814)Termination reason: Instruction limit
% 3.99/0.95 % (3651814)Termination phase: Property scanning
% 3.99/0.95 % (3651814)Time elapsed: 0.041 s
% 3.99/0.95 % (3651814)Peak memory usage: 11 MB
% 3.99/0.95 % (3651814)Instructions burned: 104 (million)
% 3.99/0.95 % (3651815)Instruction limit reached!
% 3.99/0.95 % (3651815)------------------------------
% 3.99/0.95 % (3651815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.99/0.95 % (3651815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/0.95 % (3651815)CaDiCaL version: 2.1.3
% 3.99/0.95 % (3651815)Termination reason: Instruction limit
% 3.99/0.95 % (3651815)Termination phase: Property scanning
% 3.99/0.95 % (3651815)Time elapsed: 0.047 s
% 3.99/0.95 % (3651815)Peak memory usage: 11 MB
% 3.99/0.95 % (3651815)Instructions burned: 120 (million)
% 3.99/0.95 % (3651812)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.99/0.95 % (3651816)Instruction limit reached!
% 3.99/0.95 % (3651816)------------------------------
% 3.99/0.95 % (3651816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.99/0.95 % (3651816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/0.95 % (3651816)CaDiCaL version: 2.1.3
% 3.99/0.95 % (3651816)Termination reason: Instruction limit
% 3.99/0.95 % (3651816)Termination phase: Saturation
% 3.99/0.95 % (3651816)Time elapsed: 0.052 s
% 3.99/0.95 % (3651816)Peak memory usage: 12 MB
% 3.99/0.95 % (3651816)Instructions burned: 132 (million)
% 3.99/0.95 % Exception at run slice level
% 3.99/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.99/0.95 % (3651827)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2988859677:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.99/0.95 % (3651830)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2885224708:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.99/0.95 % (3651828)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2041876663:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.99/0.95 % (3651817)Instruction limit reached!
% 3.99/0.95 % (3651817)------------------------------
% 3.99/0.95 % (3651817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.99/0.95 % (3651817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.53/2.34 % (3651817)CaDiCaL version: 2.1.3
% 14.53/2.34 % (3651817)Termination reason: Instruction limit
% 14.53/2.34 % (3651817)Termination phase: Saturation
% 14.53/2.34 % (3651817)Time elapsed: 0.068 s
% 14.53/2.34 % (3651817)Peak memory usage: 13 MB
% 14.53/2.34 % (3651817)Instructions burned: 160 (million)
% 14.53/2.34 % (3651829)ott-21_1_sil=16000:fs=off:random_seed=3987478499:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 14.53/2.34 % (3651834)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3985860322:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 14.53/2.34 % (3651828)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.53/2.34 % (3651827)Instruction limit reached!
% 14.53/2.34 % (3651827)------------------------------
% 14.53/2.34 % (3651827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.53/2.34 % (3651827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.53/2.34 % (3651827)CaDiCaL version: 2.1.3
% 14.53/2.34 % (3651827)Termination reason: Instruction limit
% 14.53/2.34 % (3651827)Termination phase: Saturation
% 14.53/2.34 % (3651827)Time elapsed: 0.051 s
% 14.53/2.34 % (3651827)Peak memory usage: 12 MB
% 14.53/2.34 % (3651827)Instructions burned: 132 (million)
% 14.53/2.34 % (3651828)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 14.53/2.34 % (3651837)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1532451760:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 14.53/2.34 % Exception at run slice level
% 14.53/2.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.53/2.34 % (3651829)Instruction limit reached!
% 14.53/2.34 % (3651829)------------------------------
% 14.53/2.34 % (3651829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.53/2.34 % (3651829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.53/2.34 % (3651829)CaDiCaL version: 2.1.3
% 14.53/2.34 % (3651829)Termination reason: Instruction limit
% 14.53/2.34 % (3651829)Termination phase: Saturation
% 14.53/2.34 % (3651829)Time elapsed: 0.076 s
% 14.53/2.34 % (3651829)Peak memory usage: 13 MB
% 14.53/2.34 % (3651829)Instructions burned: 181 (million)
% 14.53/2.34 % (3651839)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1440267943:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 14.53/2.34 % (3651840)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=4092879706:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 14.53/2.34 % (3651830)Instruction limit reached!
% 14.53/2.34 % (3651830)------------------------------
% 14.53/2.34 % (3651830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.53/2.34 % (3651830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.53/2.34 % (3651830)CaDiCaL version: 2.1.3
% 14.53/2.34 % (3651830)Termination reason: Instruction limit
% 14.53/2.34 % (3651830)Termination phase: Saturation
% 14.53/2.34 % (3651830)Time elapsed: 0.118 s
% 14.53/2.34 % (3651830)Peak memory usage: 15 MB
% 14.53/2.34 % (3651830)Instructions burned: 479 (million)
% 14.53/2.34 % (3651840)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.53/2.34 % (3651843)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1147847628:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 14.53/2.34 % (3651843)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.53/2.34 % Exception at run slice level
% 14.53/2.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.53/2.34 % (3651845)fmb+10_1_sil=64000:random_seed=1918752309:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 14.53/2.34 % (3651845)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 14.53/2.34 % Exception at run slice level
% 14.53/2.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.53/2.34 % (3651847)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3313730070:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 14.53/2.34 % Exception at run slice level
% 14.53/2.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.57/2.78 % (3651849)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4016347192:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 16.57/2.78 % (3651828)Instruction limit reached!
% 16.57/2.78 % (3651828)------------------------------
% 16.57/2.78 % (3651828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651828)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651828)Termination reason: Instruction limit
% 16.57/2.78 % (3651828)Termination phase: Saturation
% 16.57/2.78 % (3651828)Time elapsed: 0.319 s
% 16.57/2.78 % (3651828)Peak memory usage: 16 MB
% 16.57/2.78 % (3651828)Instructions burned: 684 (million)
% 16.57/2.78 % (3651851)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=21807435:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 16.57/2.78 % Exception at run slice level
% 16.57/2.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.57/2.78 % (3651843)Instruction limit reached!
% 16.57/2.78 % (3651843)------------------------------
% 16.57/2.78 % (3651843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651843)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651843)Termination reason: Instruction limit
% 16.57/2.78 % (3651843)Termination phase: Saturation
% 16.57/2.78 % (3651843)Time elapsed: 0.230 s
% 16.57/2.78 % (3651843)Peak memory usage: 17 MB
% 16.57/2.78 % (3651843)Instructions burned: 882 (million)
% 16.57/2.78 % (3651851)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.57/2.78 % (3651853)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3590117513:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 16.57/2.78 % (3651854)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2636458669:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 16.57/2.78 % (3651840)Instruction limit reached!
% 16.57/2.78 % (3651840)------------------------------
% 16.57/2.78 % (3651840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651840)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651840)Termination reason: Instruction limit
% 16.57/2.78 % (3651840)Termination phase: Saturation
% 16.57/2.78 % (3651840)Time elapsed: 0.288 s
% 16.57/2.78 % (3651840)Peak memory usage: 15 MB
% 16.57/2.78 % (3651840)Instructions burned: 693 (million)
% 16.57/2.78 % Exception at run slice level
% 16.57/2.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.57/2.78 % (3651853)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 16.57/2.78 % (3651858)ott-2_1_sil=16000:newcnf=on:random_seed=4070302591:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 16.57/2.78 % (3651857)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3046625182:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 16.57/2.78 % (3651853)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.57/2.78 % (3651858)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.57/2.78 % Exception at run slice level
% 16.57/2.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.57/2.78 % (3651861)ott+10_1_sil=32000:tgt=ground:random_seed=4134346198:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 16.57/2.78 % (3651837)Instruction limit reached!
% 16.57/2.78 % (3651837)------------------------------
% 16.57/2.78 % (3651837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651837)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651837)Termination reason: Instruction limit
% 16.57/2.78 % (3651837)Termination phase: Saturation
% 16.57/2.78 % (3651837)Time elapsed: 0.471 s
% 16.57/2.78 % (3651837)Peak memory usage: 15 MB
% 16.57/2.78 % (3651837)Instructions burned: 1180 (million)
% 16.57/2.78 % (3651863)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=101501961:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 16.57/2.78 % (3651858)Instruction limit reached!
% 16.57/2.78 % (3651858)------------------------------
% 16.57/2.78 % (3651858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651858)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651858)Termination reason: Instruction limit
% 16.57/2.78 % (3651858)Termination phase: Saturation
% 16.57/2.78 % (3651858)Time elapsed: 0.189 s
% 16.57/2.78 % (3651858)Peak memory usage: 15 MB
% 16.57/2.78 % (3651858)Instructions burned: 869 (million)
% 16.57/2.78 % Exception at run slice level
% 16.57/2.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.57/2.78 % (3651865)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3991760711:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 16.57/2.78 % (3651866)dis+21_1_sil=32000:sas=cadical:random_seed=3528667147:i=3773:amm=off_2992 on theBenchmark for (2992ds/3773Mi)
% 16.57/2.78 % (3651865)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.57/2.78 % (3651853)Instruction limit reached!
% 16.57/2.78 % (3651853)------------------------------
% 16.57/2.78 % (3651853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651853)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651853)Termination reason: Instruction limit
% 16.57/2.78 % (3651853)Termination phase: Saturation
% 16.57/2.78 % (3651853)Time elapsed: 0.659 s
% 16.57/2.78 % (3651853)Peak memory usage: 18 MB
% 16.57/2.78 % (3651853)Instructions burned: 1473 (million)
% 16.57/2.78 % (3651869)ott+11_1_sil=16000:gs=on:random_seed=4107606229:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 16.57/2.78 % (3651869)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.57/2.78 % (3651865)Instruction limit reached!
% 16.57/2.78 % (3651865)------------------------------
% 16.57/2.78 % (3651865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651865)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651865)Termination reason: Instruction limit
% 16.57/2.78 % (3651865)Termination phase: Saturation
% 16.57/2.78 % (3651865)Time elapsed: 0.756 s
% 16.57/2.78 % (3651865)Peak memory usage: 22 MB
% 16.57/2.78 % (3651865)Instructions burned: 3514 (million)
% 16.57/2.78 % (3651871)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3106594531:fmbsr=1.6:i=67534_2985 on theBenchmark for (2985ds/67534Mi)
% 16.57/2.78 % Exception at run slice level
% 16.57/2.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.57/2.78 % (3651873)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=3779296559:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2984 on theBenchmark for (2984ds/4591Mi)
% 16.57/2.78 % (3651861)Instruction limit reached!
% 16.57/2.78 % (3651861)------------------------------
% 16.57/2.78 % (3651861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651861)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651861)Termination reason: Instruction limit
% 16.57/2.78 % (3651861)Termination phase: Saturation
% 16.57/2.78 % (3651861)Time elapsed: 1.465 s
% 16.57/2.78 % (3651861)Peak memory usage: 14 MB
% 16.57/2.78 % (3651861)Instructions burned: 5114 (million)
% 16.57/2.78 % (3651875)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=1287205126:i=29340_2979 on theBenchmark for (2979ds/29340Mi)
% 16.57/2.78 % (3651869)Instruction limit reached!
% 16.57/2.78 % (3651869)------------------------------
% 16.57/2.78 % (3651869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651869)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651869)Termination reason: Instruction limit
% 16.57/2.78 % (3651869)Termination phase: Saturation
% 16.57/2.78 % (3651869)Time elapsed: 0.922 s
% 16.57/2.78 % (3651869)Peak memory usage: 17 MB
% 16.57/2.78 % (3651869)Instructions burned: 2253 (million)
% 16.57/2.78 % (3651877)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=954139285:i=5211_2979 on theBenchmark for (2979ds/5211Mi)
% 16.57/2.78 % (3651866)Instruction limit reached!
% 16.57/2.78 % (3651866)------------------------------
% 16.57/2.78 % (3651866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.78 % (3651866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.78 % (3651866)CaDiCaL version: 2.1.3
% 16.57/2.78 % (3651866)Termination reason: Instruction limit
% 16.57/2.78 % (3651866)Termination phase: Saturation
% 16.57/2.78 % (3651866)Time elapsed: 1.600 s
% 16.57/2.78 % (3651866)Peak memory usage: 20 MB
% 16.57/2.78 % (3651866)Instructions burned: 3776 (million)
% 16.57/2.78 % (3651879)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=756405830:i=5497:nm=2_2976 on theBenchmark for (2976ds/5497Mi)
% 16.57/2.78 % Exception at run slice level
% 16.57/2.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.57/2.78 % (3651881)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=1496629706:fmbsr=2:i=46332_2975 on theBenchmark for (2975ds/46332Mi)
% 16.57/2.78 % Exception at run slice level
% 16.57/2.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.57/2.78 % (3651883)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=1720808386:i=14071_2975 on theBenchmark for (2975ds/14071Mi)
% 16.57/2.78 % (3651812) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3651806-3651812"...
% 16.57/2.78 % (3651812)...printing done.
% 16.57/2.78 % (3651812)Refutation found. Thanks to Tanya!
% 16.57/2.78 % SZS status Theorem for theBenchmark
% 16.57/2.78 % SZS output start Proof for theBenchmark
% 16.57/2.78 thf(type_def_5, type, partia1265057091ct_ext: ($tType * $tType) > $tType).
% 16.57/2.78 thf(type_def_6, type, monoid_ext: ($tType * $tType) > $tType).
% 16.57/2.78 thf(type_def_7, type, ring_ext: ($tType * $tType) > $tType).
% 16.57/2.78 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 16.57/2.78 thf(type_def_9, type, set: $tType > $tType).
% 16.57/2.78 thf(type_def_10, type, int: $tType).
% 16.57/2.78 thf(type_def_11, type, b: $tType).
% 16.57/2.78 thf(type_def_12, type, a: $tType).
% 16.57/2.78 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 16.57/2.78 thf(func_def_0, type, group_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_1, type, ab_group_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_2, type, semigroup_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_3, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_4, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_5, type, linordered_semidom: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_6, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_7, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_8, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_9, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_10, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_11, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_12, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_13, type, ordere623563068d_diff: !>[X0: $tType]:($o)).
% 16.57/2.78 thf(func_def_14, type, a_l_coset: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > set @ X0 > set @ X0))).
% 16.57/2.78 thf(func_def_15, type, additive_subgroup: !>[X0: $tType, X1: $tType]:((set @ X0 > partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 16.57/2.78 thf(func_def_16, type, set_add: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > set @ X0 > set @ X0))).
% 16.57/2.78 thf(func_def_17, type, partial_carrier: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ X1 > set @ X0))).
% 16.57/2.78 thf(func_def_18, type, mult: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0 > X0 > X0))).
% 16.57/2.78 thf(func_def_19, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 16.57/2.78 thf(func_def_20, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 16.57/2.78 thf(func_def_21, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 16.57/2.78 thf(func_def_22, type, locali1648044335f_frac: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 16.57/2.78 thf(func_def_23, type, locali7914339f_crng: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 16.57/2.78 thf(func_def_24, type, locali1402578320of_rng: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 16.57/2.78 thf(func_def_25, type, locali1441642228monoid: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > set @ X0 > $o))).
% 16.57/2.78 thf(func_def_26, type, bot_bot: !>[X0: $tType]:(X0)).
% 16.57/2.78 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 16.57/2.78 thf(func_def_28, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 16.57/2.78 thf(func_def_29, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 16.57/2.78 thf(func_def_30, type, a_inv: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > X0))).
% 16.57/2.78 thf(func_def_31, type, a_minus: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > X0 > X0))).
% 16.57/2.78 thf(func_def_32, type, add_pow: !>[X0: $tType, X1: $tType, X2: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X2 > X0 > X0))).
% 16.57/2.78 thf(func_def_33, type, add: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > X0 > X0))).
% 16.57/2.78 thf(func_def_34, type, zero: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0))).
% 16.57/2.78 thf(func_def_35, type, semiring: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 16.57/2.78 thf(func_def_36, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 16.57/2.78 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 16.57/2.78 thf(func_def_38, type, r: partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b).
% 16.57/2.78 thf(func_def_39, type, s: set @ a).
% 16.57/2.78 thf(func_def_40, type, r2: a).
% 16.57/2.78 thf(func_def_41, type, r3: a).
% 16.57/2.78 thf(func_def_42, type, s2: a).
% 16.57/2.78 thf(func_def_43, type, s3: a).
% 16.57/2.78 thf(func_def_44, type, t: a).
% 16.57/2.78 thf(func_def_45, type, t2: a).
% 16.57/2.78 thf(func_def_46, type, x: product_prod @ a @ a).
% 16.57/2.78 thf(func_def_47, type, y: product_prod @ a @ a).
% 16.57/2.78 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 16.57/2.78 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 16.57/2.78 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 16.57/2.78 thf(func_def_54, type, db1: !>[X0: $tType]:(X0)).
% 16.57/2.78 thf(func_def_55, type, vAND: ($o > $o > $o)).
% 16.57/2.78 thf(func_def_56, type, db2: !>[X0: $tType]:(X0)).
% 16.57/2.78 thf(func_def_57, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 16.57/2.78 thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 16.57/2.78 thf(func_def_59, type, vNOT: ($o > $o)).
% 16.57/2.78 thf(func_def_60, type, vIMP: ($o > $o > $o)).
% 16.57/2.78 thf(func_def_61, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 16.57/2.78 thf(func_def_62, type, sK1: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 16.57/2.78 thf(func_def_63, type, sK2: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 16.57/2.78 thf(func_def_64, type, sK3: (a > a)).
% 16.57/2.78 thf(func_def_65, type, sK4: (a > a)).
% 16.57/2.78 thf(func_def_66, type, sK5: (a > a)).
% 16.57/2.78 thf(func_def_67, type, sK6: a).
% 16.57/2.78 thf(func_def_68, type, sK7: a).
% 16.57/2.78 thf(func_def_69, type, sK8: !>[X0: $tType]:((X0 > X0 > X0))).
% 16.57/2.79 thf(func_def_70, type, sK9: (set @ a > a)).
% 16.57/2.79 thf(func_def_71, type, sK10: (set @ a > a)).
% 16.57/2.79 thf(func_def_72, type, sK11: (set @ a > a)).
% 16.57/2.79 thf(func_def_73, type, sK12: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 16.57/2.79 thf(func_def_74, type, sK13: !>[X0: $tType]:((set @ X0 > X0))).
% 16.57/2.79 thf(func_def_75, type, sK14: !>[X0: $tType]:((set @ X0 > X0))).
% 16.57/2.79 thf(func_def_76, type, sK15: !>[X0: $tType]:(((X0 > $o) > X0))).
% 16.57/2.79 thf(func_def_77, type, sK16: !>[X0: $tType]:(((X0 > $o) > X0))).
% 16.57/2.79 thf(func_def_78, type, sK17: !>[X0: $tType]:((set @ X0 > X0))).
% 16.57/2.79 thf(func_def_80, type, sK19: !>[X0: $tType]:(((X0 > $o) > X0))).
% 16.57/2.79 thf(func_def_81, type, sK20: !>[X0: $tType]:(((X0 > $o) > X0))).
% 16.57/2.79 thf(f13,axiom,(
% 16.57/2.79 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_f41)).
% 16.57/2.79 thf(f14,axiom,(
% 16.57/2.79 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_f42)).
% 16.57/2.79 thf(f22,axiom,(
% 16.57/2.79 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062)).
% 16.57/2.79 thf(f42,axiom,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x)))))) = ((a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_f25)).
% 16.57/2.79 thf(f43,axiom,(
% 16.57/2.79 (((a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_f32)).
% 16.57/2.79 thf(f49,axiom,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y)))))) = ((a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_f30)).
% 16.57/2.79 thf(f50,axiom,(
% 16.57/2.79 (((a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_f33)).
% 16.57/2.79 thf(f58,axiom,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) = ((zero @ a @ b @ r)))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_f5)).
% 16.57/2.79 thf(f59,axiom,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))) = ((zero @ a @ b @ r)))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_f7)).
% 16.57/2.79 thf(f66,axiom,(
% 16.57/2.79 (member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ s)),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_f8)).
% 16.57/2.79 thf(f131,axiom,(
% 16.57/2.79 ! [X0 : $tType,X1 : $tType] : (a_minus @ X1 @ X0 = (^[X2 : partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ ring_ext @ X1 @ X0, X3 : X1, X4 : X1] : ((add @ X1 @ X0 @ X2 @ X3 @ (a_inv @ X1 @ X0 @ X2 @ X4)))))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_a__minus__def)).
% 16.57/2.79 thf(f143,axiom,(
% 16.57/2.79 (ord_less_eq @ set @ a @ s @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_subset)).
% 16.57/2.79 thf(f253,axiom,(
% 16.57/2.79 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((member @ X0 @ X3 @ X1) => (member @ X0 @ X3 @ X2)))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_in__mono)).
% 16.57/2.79 thf(f269,conjecture,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 16.57/2.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 16.57/2.79 thf(f270,negated_conjecture,(
% 16.57/2.79 ~ (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 16.57/2.79 inference(negated_conjecture,[status(cth)],[f269])).
% 16.57/2.79 thf(f291,plain,(
% 16.57/2.79 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 16.57/2.79 inference(rectify,[],[f13])).
% 16.57/2.79 thf(f292,plain,(
% 16.57/2.79 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 inference(fool_elimination,[],[f291])).
% 16.57/2.79 thf(f293,plain,(
% 16.57/2.79 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 16.57/2.79 inference(rectify,[],[f14])).
% 16.57/2.79 thf(f294,plain,(
% 16.57/2.79 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 inference(fool_elimination,[],[f293])).
% 16.57/2.79 thf(f307,plain,(
% 16.57/2.79 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))))),
% 16.57/2.79 inference(rectify,[],[f22])).
% 16.57/2.79 thf(f308,plain,(
% 16.57/2.79 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) => ((((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) => ((((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) => (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))))),
% 16.57/2.79 inference(fool_elimination,[],[f307])).
% 16.57/2.79 thf(f351,plain,(
% 16.57/2.79 (member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ s)),
% 16.57/2.79 inference(rectify,[],[f66])).
% 16.57/2.79 thf(f352,plain,(
% 16.57/2.79 (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ s)) = $true)),
% 16.57/2.79 inference(fool_elimination,[],[f351])).
% 16.57/2.79 thf(f470,plain,(
% 16.57/2.79 ! [X0 : $tType,X1 : $tType] : (a_minus @ X1 @ X0 = (^[Y0 : partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ ring_ext @ X1 @ X0]: ((^[Y1 : X1]: ((^[Y2 : X1]: (add @ X1 @ X0 @ Y0 @ Y1 @ (a_inv @ X1 @ X0 @ Y0 @ Y2))))))))),
% 16.57/2.79 inference(fool_elimination,[],[f131])).
% 16.57/2.79 thf(f493,plain,(
% 16.57/2.79 (ord_less_eq @ set @ a @ s @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 16.57/2.79 inference(rectify,[],[f143])).
% 16.57/2.79 thf(f494,plain,(
% 16.57/2.79 (((ord_less_eq @ set @ a @ s @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 inference(fool_elimination,[],[f493])).
% 16.57/2.79 thf(f701,plain,(
% 16.57/2.79 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((member @ X0 @ X3 @ X1) => (member @ X0 @ X3 @ X2)))),
% 16.57/2.79 inference(rectify,[],[f253])).
% 16.57/2.79 thf(f702,plain,(
% 16.57/2.79 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((((ord_less_eq @ set @ X0 @ X1 @ X2)) = $true) => ((((member @ X0 @ X3 @ X1)) = $true) => (((member @ X0 @ X3 @ X2)) = $true)))),
% 16.57/2.79 inference(fool_elimination,[],[f701])).
% 16.57/2.79 thf(f739,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) != ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 16.57/2.79 inference(flattening,[],[f270])).
% 16.57/2.79 thf(f762,plain,(
% 16.57/2.79 (((((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)),
% 16.57/2.79 inference(ennf_transformation,[],[f308])).
% 16.57/2.79 thf(f763,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)),
% 16.57/2.79 inference(flattening,[],[f762])).
% 16.57/2.79 thf(f989,plain,(
% 16.57/2.79 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : (((((member @ X0 @ X3 @ X2)) = $true) | (((member @ X0 @ X3 @ X1)) != $true)) | (((ord_less_eq @ set @ X0 @ X1 @ X2)) != $true))),
% 16.57/2.79 inference(ennf_transformation,[],[f702])).
% 16.57/2.79 thf(f990,plain,(
% 16.57/2.79 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((((member @ X0 @ X3 @ X2)) = $true) | (((member @ X0 @ X3 @ X1)) != $true) | (((ord_less_eq @ set @ X0 @ X1 @ X2)) != $true))),
% 16.57/2.79 inference(flattening,[],[f989])).
% 16.57/2.79 thf(f1018,plain,(
% 16.57/2.79 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 inference(cnf_transformation,[],[f292])).
% 16.57/2.79 thf(f1019,plain,(
% 16.57/2.79 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 inference(cnf_transformation,[],[f294])).
% 16.57/2.79 thf(f1027,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)),
% 16.57/2.79 inference(cnf_transformation,[],[f763])).
% 16.57/2.79 thf(f1047,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x)))))) = ((a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))))),
% 16.57/2.79 inference(cnf_transformation,[],[f42])).
% 16.57/2.79 thf(f1048,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))) = ((a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))))),
% 16.57/2.79 inference(cnf_transformation,[],[f43])).
% 16.57/2.79 thf(f1054,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y)))))) = ((a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))),
% 16.57/2.79 inference(cnf_transformation,[],[f49])).
% 16.57/2.79 thf(f1055,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))) = ((a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))),
% 16.57/2.79 inference(cnf_transformation,[],[f50])).
% 16.57/2.79 thf(f1063,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) = ((zero @ a @ b @ r)))),
% 16.57/2.79 inference(cnf_transformation,[],[f58])).
% 16.57/2.79 thf(f1064,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))) = ((zero @ a @ b @ r)))),
% 16.57/2.79 inference(cnf_transformation,[],[f59])).
% 16.57/2.79 thf(f1071,plain,(
% 16.57/2.79 (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ s)) = $true)),
% 16.57/2.79 inference(cnf_transformation,[],[f352])).
% 16.57/2.79 thf(f1141,plain,(
% 16.57/2.79 ( ! [X1 : $tType,X0 : $tType] : ((a_minus @ X1 @ X0 = (^[Y0 : partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ ring_ext @ X1 @ X0]: ((^[Y1 : X1]: ((^[Y2 : X1]: (add @ X1 @ X0 @ Y0 @ Y1 @ (a_inv @ X1 @ X0 @ Y0 @ Y2))))))))) )),
% 16.57/2.79 inference(cnf_transformation,[],[f470])).
% 16.57/2.79 thf(f1153,plain,(
% 16.57/2.79 (((ord_less_eq @ set @ a @ s @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 inference(cnf_transformation,[],[f494])).
% 16.57/2.79 thf(f1269,plain,(
% 16.57/2.79 ( ! [X0 : $tType,X2 : set @ X0,X3 : X0,X1 : set @ X0] : ((((ord_less_eq @ set @ X0 @ X1 @ X2)) != $true) | (((member @ X0 @ X3 @ X1)) != $true) | (((member @ X0 @ X3 @ X2)) = $true)) )),
% 16.57/2.79 inference(cnf_transformation,[],[f990])).
% 16.57/2.79 thf(f1286,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) != ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 16.57/2.79 inference(cnf_transformation,[],[f739])).
% 16.57/2.79 thf(f1290,plain,(
% 16.57/2.79 ($true = ((member @ a @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1018,f1141])).
% 16.57/2.79 thf(f1291,plain,(
% 16.57/2.79 ($true = ((member @ a @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1019,f1141])).
% 16.57/2.79 thf(f1295,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | ($true != ((member @ a @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)))) | ($true != ((member @ a @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1027,f1141,f1141,f1141,f1141,f1141,f1141])).
% 16.57/2.79 thf(f1300,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x)))))) = (((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1047,f1141,f1141])).
% 16.57/2.79 thf(f1301,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))) = (((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1048,f1141,f1141])).
% 16.57/2.79 thf(f1304,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y)))))) = (((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1054,f1141,f1141])).
% 16.57/2.79 thf(f1305,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))) = (((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1055,f1141,f1141])).
% 16.57/2.79 thf(f1311,plain,(
% 16.57/2.79 (((zero @ a @ b @ r)) = ((mult @ a @ ring_ext @ a @ b @ r @ t2 @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1063,f1141])).
% 16.57/2.79 thf(f1312,plain,(
% 16.57/2.79 (((zero @ a @ b @ r)) = ((mult @ a @ ring_ext @ a @ b @ r @ t @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1064,f1141])).
% 16.57/2.79 thf(f1318,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) != ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ ((^[Y0 : partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b]: ((^[Y1 : a]: ((^[Y2 : a]: (add @ a @ b @ Y0 @ Y1 @ (a_inv @ a @ b @ Y0 @ Y2))))))) @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 16.57/2.79 inference(definition_unfolding,[],[f1286,f1141,f1141,f1141,f1141])).
% 16.57/2.79 thf(f1335,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x)))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y)))))))) != ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1318])).
% 16.57/2.79 thf(f1539,plain,(
% 16.57/2.79 (((zero @ a @ b @ r)) = ((mult @ a @ ring_ext @ a @ b @ r @ t @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y)))))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1312])).
% 16.57/2.79 thf(f1540,plain,(
% 16.57/2.79 (((zero @ a @ b @ r)) = ((mult @ a @ ring_ext @ a @ b @ r @ t2 @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x)))))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1311])).
% 16.57/2.79 thf(f1546,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1305])).
% 16.57/2.79 thf(f1547,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1304])).
% 16.57/2.79 thf(f1554,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1301])).
% 16.57/2.79 thf(f1555,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1300])).
% 16.57/2.79 thf(f1560,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | ($true != ((member @ a @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)))) | ($true != ((member @ a @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1295])).
% 16.57/2.79 thf(f1564,plain,(
% 16.57/2.79 ($true = ((member @ a @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1291])).
% 16.57/2.79 thf(f1565,plain,(
% 16.57/2.79 ($true = ((member @ a @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 16.57/2.79 inference(beta-eta_normalization,[],[f1290])).
% 16.57/2.79 thf(f1567,definition,(
% 16.57/2.79 spl18_1 <=> ($true = ((member @ a @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 16.57/2.79 introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition])).
% 16.57/2.79 thf(f1571,definition,(
% 16.57/2.79 spl18_2 <=> ($true = ((member @ a @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 16.57/2.79 introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition])).
% 16.57/2.79 thf(f1575,definition,(
% 16.57/2.79 spl18_3 <=> (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition])).
% 16.57/2.79 thf(f1577,plain,(
% 16.57/2.79 (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | spl18_3),
% 16.57/2.79 inference(avatar_component_clause,[],[f1575])).
% 16.57/2.79 thf(f1579,definition,(
% 16.57/2.79 spl18_4 <=> (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))))),
% 16.57/2.79 introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition])).
% 16.57/2.79 thf(f1581,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))) | ~spl18_4),
% 16.57/2.79 inference(avatar_component_clause,[],[f1579])).
% 16.57/2.79 thf(f1582,plain,(
% 16.57/2.79 ~spl18_1 | ~spl18_2 | ~spl18_3 | spl18_4),
% 16.57/2.79 inference(avatar_split_clause,[],[f1560,f1579,f1575,f1571,f1567])).
% 16.57/2.79 thf(f1583,plain,(
% 16.57/2.79 spl18_2),
% 16.57/2.79 inference(avatar_split_clause,[],[f1564,f1571])).
% 16.57/2.79 thf(f1584,plain,(
% 16.57/2.79 spl18_1),
% 16.57/2.79 inference(avatar_split_clause,[],[f1565,f1567])).
% 16.57/2.79 thf(f2138,plain,(
% 16.57/2.79 ( ! [X0 : a] : (($true != $true) | (((member @ a @ X0 @ s)) != $true) | (((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)) )),
% 16.57/2.79 inference(constrained_superposition,[],[f1269,f1153])).
% 16.57/2.79 thf(f2139,plain,(
% 16.57/2.79 ( ! [X0 : a] : ((((member @ a @ X0 @ s)) != $true) | (((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)) )),
% 16.57/2.79 inference(trivial_inequality_removal,[],[f2138])).
% 16.57/2.79 thf(f15687,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3))) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (zero @ a @ b @ r))))),
% 16.57/2.79 inference(forward_demodulation,[],[f1547,f1539])).
% 16.57/2.79 thf(f15772,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2))) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r))))),
% 16.57/2.79 inference(forward_demodulation,[],[f1555,f1540])).
% 16.57/2.79 thf(f16027,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (zero @ a @ b @ r))))),
% 16.57/2.79 inference(forward_demodulation,[],[f1546,f15687])).
% 16.57/2.79 thf(f16081,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r))))),
% 16.57/2.79 inference(forward_demodulation,[],[f1554,f15772])).
% 16.57/2.79 thf(f33499,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))) | ~spl18_4),
% 16.57/2.79 inference(forward_demodulation,[],[f1581,f16081])).
% 16.57/2.79 thf(f34673,plain,(
% 16.57/2.79 (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (zero @ a @ b @ r))))) | ~spl18_4),
% 16.57/2.79 inference(forward_demodulation,[],[f33499,f16027])).
% 16.57/2.79 thf(f34914,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x)))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y)))))))) != ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (zero @ a @ b @ r))))) | ~spl18_4),
% 16.57/2.79 inference(constrained_superposition,[],[f1335,f34673])).
% 16.57/2.79 thf(f34915,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (zero @ a @ b @ r)))) != ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (a_inv @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))))) | ~spl18_4),
% 16.57/2.79 inference(forward_demodulation,[],[f34914,f1540])).
% 16.57/2.79 thf(f34916,plain,(
% 16.57/2.79 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (zero @ a @ b @ r)))) != ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (zero @ a @ b @ r)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (zero @ a @ b @ r))))) | ~spl18_4),
% 16.57/2.79 inference(forward_demodulation,[],[f34915,f1539])).
% 16.57/2.79 thf(f34917,plain,(
% 16.57/2.79 $false | ~spl18_4),
% 16.57/2.79 inference(trivial_inequality_removal,[],[f34916])).
% 16.57/2.79 thf(f34918,plain,(
% 16.57/2.79 ~spl18_4),
% 16.57/2.79 inference(avatar_contradiction_clause,[],[f34917])).
% 16.57/2.79 thf(f41938,plain,(
% 16.57/2.79 ($true != $true) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 inference(constrained_superposition,[],[f2139,f1071])).
% 16.57/2.79 thf(f41972,plain,(
% 16.57/2.79 (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 16.57/2.79 inference(trivial_inequality_removal,[],[f41938])).
% 16.57/2.79 thf(f41980,plain,(
% 16.57/2.79 $false | spl18_3),
% 16.57/2.79 inference(forward_subsumption_resolution,[],[f41972,f1577])).
% 16.57/2.79 thf(f41981,plain,(
% 16.57/2.79 spl18_3),
% 16.57/2.79 inference(avatar_contradiction_clause,[],[f41980])).
% 16.57/2.79 cnf(s1, plain, ~spl18_1 | ~spl18_2 | ~spl18_3 | spl18_4, inference(sat_conversion,[],[f1582])).
% 16.57/2.79 cnf(s2, plain, spl18_2, inference(sat_conversion,[],[f1583])).
% 16.57/2.79 cnf(s3, plain, spl18_1, inference(sat_conversion,[],[f1584])).
% 16.57/2.79 cnf(s1254, plain, ~spl18_4, inference(sat_conversion,[],[f34918])).
% 16.57/2.79 cnf(s1378, plain, spl18_3, inference(sat_conversion,[],[f41981])).
% 16.57/2.79 cnf(s1381, plain, $false, inference(rat,[],[s1,s1254,s1378,s2,s3])).
% 16.57/2.79 thf(f41985,plain,(
% 16.57/2.79 $false),
% 16.57/2.79 inference(avatar_sat_refutation,[],[s1381])).
% 16.57/2.79 % SZS output end Proof for theBenchmark
% 16.57/2.79 % (3651812)------------------------------
% 16.57/2.79 % (3651812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.57/2.79 % (3651812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.57/2.79 % (3651812)CaDiCaL version: 2.1.3
% 16.57/2.79 % (3651812)Termination reason: Refutation
% 16.57/2.79 % (3651812)Time elapsed: 2.488 s
% 16.57/2.79 % (3651812)Peak memory usage: 26 MB
% 16.57/2.79 % (3651812)Instructions burned: 5698 (million)
% 16.57/2.79 % (3651806)Success in time 2.552 s
% 16.57/2.79 % Vampire exiting
%------------------------------------------------------------------------------