%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT208^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 07:49:02 AM UTC 2026
% Result : Theorem 9.09s 1.78s
% Output : Refutation 9.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT208^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n013.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 18:08:21 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
% 5.69/1.08 % (2462165)Will run a generic schedule for satisfiability detection.
% 5.69/1.08 % (2462172)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2302222849:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.69/1.08 % (2462171)% WARNING: option uhcvi not known.
% 5.69/1.08 % (2462170)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1009737045_2999 on theBenchmark for (2999ds/0Mi)
% 5.69/1.08 % (2462171)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=236860281:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.69/1.08 % (2462173)dis+10_1_sil=32000:sp=arity:random_seed=3453864980:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.69/1.08 % (2462174)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=641168323:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.69/1.08 % (2462175)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=827138556:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.69/1.08 % (2462176)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=681912281:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.69/1.08 % (2462171)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.69/1.08 % (2462174)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.69/1.08 % Exception at run slice level
% 5.69/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.69/1.08 % (2462171)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.69/1.08 % (2462173)Instruction limit reached!
% 5.69/1.08 % (2462173)------------------------------
% 5.69/1.08 % (2462173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.69/1.08 % (2462173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.69/1.08 % (2462173)CaDiCaL version: 2.1.3
% 5.69/1.08 % (2462173)Termination reason: Instruction limit
% 5.69/1.08 % (2462173)Termination phase: Saturation
% 5.69/1.08 % (2462173)Time elapsed: 0.044 s
% 5.69/1.08 % (2462173)Peak memory usage: 12 MB
% 5.69/1.08 % (2462173)Instructions burned: 104 (million)
% 5.69/1.08 % (2462174)Instruction limit reached!
% 5.69/1.08 % (2462174)------------------------------
% 5.69/1.08 % (2462174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.69/1.08 % (2462174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.69/1.08 % (2462174)CaDiCaL version: 2.1.3
% 5.69/1.08 % (2462174)Termination reason: Instruction limit
% 5.69/1.08 % (2462174)Termination phase: Saturation
% 5.69/1.08 % (2462174)Time elapsed: 0.050 s
% 5.69/1.08 % (2462174)Peak memory usage: 13 MB
% 5.69/1.08 % (2462174)Instructions burned: 116 (million)
% 5.69/1.08 % (2462184)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3773184944:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.69/1.08 % (2462185)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3514614034:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.69/1.08 % (2462176)Instruction limit reached!
% 5.69/1.08 % (2462176)------------------------------
% 5.69/1.08 % (2462176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.69/1.08 % (2462176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.69/1.08 % (2462176)CaDiCaL version: 2.1.3
% 5.69/1.08 % (2462176)Termination reason: Instruction limit
% 5.69/1.08 % (2462176)Termination phase: Saturation
% 5.69/1.08 % (2462176)Time elapsed: 0.070 s
% 5.69/1.08 % (2462176)Peak memory usage: 14 MB
% 5.69/1.08 % (2462176)Instructions burned: 160 (million)
% 5.69/1.08 % (2462186)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=3534697160:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.69/1.08 % (2462175)Instruction limit reached!
% 5.69/1.08 % (2462175)------------------------------
% 5.69/1.08 % (2462175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.69/1.08 % (2462175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.69/1.08 % (2462175)CaDiCaL version: 2.1.3
% 5.69/1.08 % (2462175)Termination reason: Instruction limit
% 5.69/1.08 % (2462175)Termination phase: Saturation
% 5.69/1.08 % (2462175)Time elapsed: 0.075 s
% 5.69/1.08 % (2462175)Peak memory usage: 13 MB
% 5.69/1.08 % (2462175)Instructions burned: 132 (million)
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % (2462189)ott-21_1_sil=16000:fs=off:random_seed=1509365942:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 9.09/1.78 % (2462186)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.09/1.78 % (2462191)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1317042564:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 9.09/1.78 % (2462193)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=605611675:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 9.09/1.78 % (2462186)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 9.09/1.78 % (2462185)Instruction limit reached!
% 9.09/1.78 % (2462185)------------------------------
% 9.09/1.78 % (2462185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462185)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462185)Termination reason: Instruction limit
% 9.09/1.78 % (2462185)Termination phase: Saturation
% 9.09/1.78 % (2462185)Time elapsed: 0.058 s
% 9.09/1.78 % (2462185)Peak memory usage: 13 MB
% 9.09/1.78 % (2462185)Instructions burned: 132 (million)
% 9.09/1.78 % (2462196)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1783875126:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % (2462198)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2402591961:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 9.09/1.78 % (2462189)Instruction limit reached!
% 9.09/1.78 % (2462189)------------------------------
% 9.09/1.78 % (2462189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462189)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462189)Termination reason: Instruction limit
% 9.09/1.78 % (2462189)Termination phase: Saturation
% 9.09/1.78 % (2462189)Time elapsed: 0.081 s
% 9.09/1.78 % (2462189)Peak memory usage: 13 MB
% 9.09/1.78 % (2462189)Instructions burned: 182 (million)
% 9.09/1.78 % (2462200)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=2018511940: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)
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % (2462200)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.09/1.78 % (2462202)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2173335854:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 9.09/1.78 % (2462202)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.09/1.78 % (2462186)Instruction limit reached!
% 9.09/1.78 % (2462186)------------------------------
% 9.09/1.78 % (2462186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462186)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462186)Termination reason: Instruction limit
% 9.09/1.78 % (2462186)Termination phase: Saturation
% 9.09/1.78 % (2462186)Time elapsed: 0.355 s
% 9.09/1.78 % (2462186)Peak memory usage: 15 MB
% 9.09/1.78 % (2462186)Instructions burned: 685 (million)
% 9.09/1.78 % (2462191)Instruction limit reached!
% 9.09/1.78 % (2462191)------------------------------
% 9.09/1.78 % (2462191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462191)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462191)Termination reason: Instruction limit
% 9.09/1.78 % (2462191)Termination phase: Saturation
% 9.09/1.78 % (2462191)Time elapsed: 0.336 s
% 9.09/1.78 % (2462191)Peak memory usage: 15 MB
% 9.09/1.78 % (2462191)Instructions burned: 477 (million)
% 9.09/1.78 % (2462204)fmb+10_1_sil=64000:random_seed=4140869806:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 9.09/1.78 % (2462205)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1365081337:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 9.09/1.78 % (2462204)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % (2462208)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3409144600:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 9.09/1.78 % (2462209)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1222331784:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 9.09/1.78 % (2462209)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % (2462200)Instruction limit reached!
% 9.09/1.78 % (2462200)------------------------------
% 9.09/1.78 % (2462200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462200)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462200)Termination reason: Instruction limit
% 9.09/1.78 % (2462200)Termination phase: Saturation
% 9.09/1.78 % (2462200)Time elapsed: 0.349 s
% 9.09/1.78 % (2462200)Peak memory usage: 17 MB
% 9.09/1.78 % (2462200)Instructions burned: 693 (million)
% 9.09/1.78 % (2462212)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2776702397:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 9.09/1.78 % (2462213)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=254535770:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 9.09/1.78 % (2462212)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 9.09/1.78 % (2462212)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % (2462216)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4234521853:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % (2462202)Instruction limit reached!
% 9.09/1.78 % (2462202)------------------------------
% 9.09/1.78 % (2462202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462202)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462202)Termination reason: Instruction limit
% 9.09/1.78 % (2462202)Termination phase: Saturation
% 9.09/1.78 % (2462202)Time elapsed: 0.428 s
% 9.09/1.78 % (2462202)Peak memory usage: 18 MB
% 9.09/1.78 % (2462202)Instructions burned: 879 (million)
% 9.09/1.78 % (2462218)ott-2_1_sil=16000:newcnf=on:random_seed=4027864196:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 9.09/1.78 % (2462219)ott+10_1_sil=32000:tgt=ground:random_seed=3235543575:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 9.09/1.78 % (2462218)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.09/1.78 % (2462196)Instruction limit reached!
% 9.09/1.78 % (2462196)------------------------------
% 9.09/1.78 % (2462196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462196)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462196)Termination reason: Instruction limit
% 9.09/1.78 % (2462196)Termination phase: Saturation
% 9.09/1.78 % (2462196)Time elapsed: 0.598 s
% 9.09/1.78 % (2462196)Peak memory usage: 18 MB
% 9.09/1.78 % (2462196)Instructions burned: 1179 (million)
% 9.09/1.78 % (2462222)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2065837617:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 9.09/1.78 % Exception at run slice level
% 9.09/1.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.09/1.78 % (2462224)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3409552357:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 9.09/1.78 % (2462224)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 9.09/1.78 % (2462218)Instruction limit reached!
% 9.09/1.78 % (2462218)------------------------------
% 9.09/1.78 % (2462218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462218)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462218)Termination reason: Instruction limit
% 9.09/1.78 % (2462218)Termination phase: Saturation
% 9.09/1.78 % (2462218)Time elapsed: 0.402 s
% 9.09/1.78 % (2462218)Peak memory usage: 17 MB
% 9.09/1.78 % (2462218)Instructions burned: 869 (million)
% 9.09/1.78 % (2462226)dis+21_1_sil=32000:sas=cadical:random_seed=3158989998:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 9.09/1.78 % (2462212)Instruction limit reached!
% 9.09/1.78 % (2462212)------------------------------
% 9.09/1.78 % (2462212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.78 % (2462212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.78 % (2462212)CaDiCaL version: 2.1.3
% 9.09/1.78 % (2462212)Termination reason: Instruction limit
% 9.09/1.78 % (2462212)Termination phase: Saturation
% 9.09/1.78 % (2462212)Time elapsed: 0.659 s
% 9.09/1.78 % (2462212)Peak memory usage: 16 MB
% 9.09/1.78 % (2462212)Instructions burned: 1473 (million)
% 9.09/1.78 % (2462228)ott+11_1_sil=16000:gs=on:random_seed=2825954753:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 9.09/1.78 % (2462228)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 9.09/1.78 % (2462228) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2462165-2462228"...
% 9.09/1.78 % (2462228)...printing done.
% 9.09/1.78 % (2462228)Refutation found. Thanks to Tanya!
% 9.09/1.78 % SZS status Theorem for theBenchmark
% 9.09/1.78 % SZS output start Proof for theBenchmark
% 9.09/1.78 thf(type_def_5, type, list: $tType > $tType).
% 9.09/1.78 thf(type_def_6, type, set: $tType > $tType).
% 9.09/1.78 thf(type_def_7, type, itself: $tType > $tType).
% 9.09/1.78 thf(type_def_8, type, a: $tType).
% 9.09/1.78 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 9.09/1.78 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_3, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_4, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_5, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_6, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_7, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_8, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_9, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_10, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_11, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_12, type, linordered_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_13, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_14, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_15, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_16, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 9.09/1.78 thf(func_def_17, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 9.09/1.78 thf(func_def_18, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 9.09/1.78 thf(func_def_19, type, coset: !>[X0: $tType]:((list @ X0 > set @ X0))).
% 9.09/1.78 thf(func_def_20, type, distinct: !>[X0: $tType]:((list @ X0 > $o))).
% 9.09/1.78 thf(func_def_21, type, linorder_sorted: !>[X0: $tType]:((list @ X0 > $o))).
% 9.09/1.78 thf(func_def_22, type, linord467138063of_set: !>[X0: $tType]:((set @ X0 > list @ X0))).
% 9.09/1.78 thf(func_def_23, type, set2: !>[X0: $tType]:((list @ X0 > set @ X0))).
% 9.09/1.78 thf(func_def_24, type, member: !>[X0: $tType]:((list @ X0 > X0 > $o))).
% 9.09/1.78 thf(func_def_25, type, union: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 9.09/1.78 thf(func_def_26, type, merge: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 9.09/1.78 thf(func_def_27, type, merges2133357844_merge: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 9.09/1.78 thf(func_def_28, type, mergesort_remdups: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 9.09/1.78 thf(func_def_29, type, sorted_by_rel: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o))).
% 9.09/1.78 thf(func_def_30, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 9.09/1.78 thf(func_def_31, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 9.09/1.78 thf(func_def_32, type, type2: !>[X0: $tType]:(itself @ X0)).
% 9.09/1.78 thf(func_def_33, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 9.09/1.78 thf(func_def_34, type, sorted763967275sorted: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 9.09/1.78 thf(func_def_35, type, sorted873716653sorted: !>[X0: $tType]:((list @ X0 > X0 > $o))).
% 9.09/1.78 thf(func_def_36, type, sorted1061247458sorted: !>[X0: $tType]:((list @ X0 > list @ X0 > $o))).
% 9.09/1.79 thf(func_def_37, type, member2: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 9.09/1.79 thf(func_def_38, type, a2: a).
% 9.09/1.79 thf(func_def_39, type, x: a).
% 9.09/1.79 thf(func_def_40, type, xsa: list @ a).
% 9.09/1.79 thf(func_def_44, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 9.09/1.79 thf(func_def_45, type, vOR: ($o > $o > $o)).
% 9.09/1.79 thf(func_def_46, type, db1: !>[X0: $tType]:(X0)).
% 9.09/1.79 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 9.09/1.79 thf(func_def_48, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 9.09/1.79 thf(func_def_49, type, vAND: ($o > $o > $o)).
% 9.09/1.79 thf(func_def_50, type, vNOT: ($o > $o)).
% 9.09/1.79 thf(func_def_51, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_52, type, vIMP: ($o > $o > $o)).
% 9.09/1.79 thf(func_def_53, type, db2: !>[X0: $tType]:(X0)).
% 9.09/1.79 thf(func_def_54, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_55, type, sP0: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_56, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 9.09/1.79 thf(func_def_57, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 9.09/1.79 thf(func_def_58, type, sP3: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 9.09/1.79 thf(func_def_59, type, sP4: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 9.09/1.79 thf(func_def_60, type, sP5: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 9.09/1.79 thf(func_def_61, type, sP6: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_62, type, sP7: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_63, type, sP8: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_64, type, sP9: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_65, type, sP10: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 9.09/1.79 thf(func_def_66, type, sP11: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 9.09/1.79 thf(func_def_67, type, sP12: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_68, type, sP13: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_69, type, sP14: !>[X0: $tType]:($o)).
% 9.09/1.79 thf(func_def_70, type, sP15: !>[X0: $tType]:((set @ X0 > $o))).
% 9.09/1.79 thf(func_def_71, type, sP16: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_72, type, sP17: !>[X0: $tType]:((set @ X0 > $o))).
% 9.09/1.79 thf(func_def_73, type, sP18: !>[X0: $tType]:((list @ X0 > (X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 9.09/1.79 thf(func_def_74, type, sP19: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 9.09/1.79 thf(func_def_75, type, sP20: !>[X0: $tType]:((list @ X0 > list @ X0 > $o))).
% 9.09/1.79 thf(func_def_76, type, sP21: $o).
% 9.09/1.79 thf(func_def_77, type, sP22: $o).
% 9.09/1.79 thf(func_def_78, type, sP23: $o).
% 9.09/1.79 thf(func_def_79, type, sK24: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_80, type, sK25: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_81, type, sK26: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_82, type, sK27: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_83, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_84, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_85, type, sK30: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_86, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_87, type, sK32: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_88, type, sK33: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_89, type, sK34: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_90, type, sK35: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_91, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_92, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_93, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_94, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_95, type, sK40: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_96, type, sK41: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_97, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_98, type, sK43: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_99, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_100, type, sK45: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_101, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_102, type, sK47: !>[X0: $tType]:(((X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_103, type, sK48: !>[X0: $tType]:((X0 > X0 > X0))).
% 9.09/1.79 thf(func_def_104, type, sK49: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_105, type, sK50: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_106, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_107, type, sK52: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_108, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_109, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_110, type, sK55: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_111, type, sK56: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_112, type, sK57: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_113, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_114, type, sK59: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_115, type, sK60: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_116, type, sK61: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_117, type, sK62: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_118, type, sK63: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_119, type, sK64: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_120, type, sK65: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_121, type, sK66: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_122, type, sK67: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_123, type, sK68: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_124, type, sK69: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 9.09/1.79 thf(func_def_125, type, sK70: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_126, type, sK71: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_127, type, sK72: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_128, type, sK73: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_129, type, sK74: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_130, type, sK75: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_131, type, sK76: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_132, type, sK77: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_133, type, sK78: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_134, type, sK79: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_135, type, sK80: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 9.09/1.79 thf(func_def_136, type, sK81: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 9.09/1.79 thf(func_def_137, type, sK82: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 9.09/1.79 thf(func_def_138, type, sK83: !>[X0: $tType]:((X0 > X0 > X0))).
% 9.09/1.79 thf(func_def_139, type, sK84: !>[X0: $tType]:((X0 > X0 > X0))).
% 9.09/1.79 thf(func_def_140, type, sK85: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_141, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 9.09/1.79 thf(func_def_142, type, sK87: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_143, type, sK88: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 9.09/1.79 thf(func_def_144, type, sK89: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_145, type, sK90: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_146, type, sK91: !>[X0: $tType]:((set @ X0 > list @ X0))).
% 9.09/1.79 thf(func_def_147, type, sK92: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_148, type, sK93: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_149, type, sK94: !>[X0: $tType]:((X0 > X0))).
% 9.09/1.79 thf(func_def_150, type, sK95: !>[X0: $tType]:((set @ X0 > list @ X0))).
% 9.09/1.79 thf(func_def_151, type, sK96: !>[X0: $tType]:((set @ X0 > list @ X0))).
% 9.09/1.79 thf(func_def_152, type, sK97: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 9.09/1.79 thf(func_def_153, type, sK98: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1 > X0))).
% 9.09/1.79 thf(func_def_154, type, sK99: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1))).
% 9.09/1.79 thf(func_def_155, type, sK100: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 9.09/1.79 thf(func_def_156, type, sK101: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_157, type, sK102: !>[X0: $tType]:((list @ X0 > (X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_158, type, sK103: !>[X0: $tType]:((list @ X0 > (X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_159, type, sK104: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 9.09/1.79 thf(func_def_160, type, sK105: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 9.09/1.79 thf(func_def_161, type, sK106: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 9.09/1.79 thf(func_def_162, type, sK107: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 9.09/1.79 thf(func_def_163, type, sK108: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 9.09/1.79 thf(func_def_164, type, sK109: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 9.09/1.79 thf(func_def_165, type, sK110: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 9.09/1.79 thf(func_def_166, type, sK111: a).
% 9.09/1.79 thf(func_def_167, type, sK112: a).
% 9.09/1.79 thf(func_def_168, type, sK113: a).
% 9.09/1.79 thf(func_def_169, type, sK114: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_170, type, sK115: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_171, type, sK116: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_172, type, sK117: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_173, type, sK118: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_174, type, sK119: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 9.09/1.79 thf(func_def_175, type, sK120: !>[X0: $tType]:((set @ X0 > list @ X0 > X0))).
% 9.09/1.79 thf(func_def_176, type, sK121: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_177, type, sK122: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 9.09/1.79 thf(func_def_178, type, sK123: !>[X0: $tType]:((list @ X0 > set @ X0 > X0))).
% 9.09/1.79 thf(f114,axiom,(
% 9.09/1.79 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : ((ord_less_eq @ X0 @ X1 @ X2) => ((X1 != X2) => (ord_less @ X0 @ X1 @ X2))))),
% 9.09/1.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_le__neq__trans)).
% 9.09/1.79 thf(f259,axiom,(
% 9.09/1.79 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => (order @ X0 @ type2 @ X0))),
% 9.09/1.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oorder)).
% 9.09/1.79 thf(f280,axiom,(
% 9.09/1.79 (linorder @ a @ type2 @ a)),
% 9.09/1.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0)).
% 9.09/1.79 thf(f282,axiom,(
% 9.09/1.79 ! [X0 : a] : ((member2 @ a @ X0 @ (set2 @ a @ xsa)) => (ord_less_eq @ a @ a2 @ X0)) & (linorder_sorted @ a @ xsa)),
% 9.09/1.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 9.09/1.79 thf(f283,axiom,(
% 9.09/1.79 (distinct @ a @ xsa) & ~(member2 @ a @ a2 @ (set2 @ a @ xsa))),
% 9.09/1.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)).
% 9.09/1.79 thf(f284,conjecture,(
% 9.09/1.79 (((! [X0 : a] : ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2) = (X0 != x) & ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2))) | (ord_less @ a @ a2 @ x)) & (! [X0 : a] : (((X0 != x) & (member2 @ a @ X0 @ (set2 @ a @ xsa))) | (X0 = a2) = (X0 != x) & ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2))) | ~(ord_less @ a @ a2 @ x))) | (x = a2)) & (! [X0 : a] : (((member2 @ a @ X0 @ (set2 @ a @ xsa))) = (X0 != a2) & ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2))) | (x != a2))),
% 9.09/1.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3)).
% 9.09/1.79 thf(f285,negated_conjecture,(
% 9.09/1.79 ~((((! [X0 : a] : ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2) = (X0 != x) & ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2))) | (ord_less @ a @ a2 @ x)) & (! [X0 : a] : (((X0 != x) & (member2 @ a @ X0 @ (set2 @ a @ xsa))) | (X0 = a2) = (X0 != x) & ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2))) | ~(ord_less @ a @ a2 @ x))) | (x = a2)) & (! [X0 : a] : (((member2 @ a @ X0 @ (set2 @ a @ xsa))) = (X0 != a2) & ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2))) | (x != a2)))),
% 9.09/1.79 inference(negated_conjecture,[status(cth)],[f284])).
% 9.09/1.79 thf(f506,plain,(
% 9.09/1.79 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : ((ord_less_eq @ X0 @ X1 @ X2) => ((X1 != X2) => (ord_less @ X0 @ X1 @ X2))))),
% 9.09/1.79 inference(rectify,[],[f114])).
% 9.09/1.79 thf(f507,plain,(
% 9.09/1.79 ! [X0 : $tType] : ((((order @ X0 @ type2 @ X0)) = $true) => ! [X1 : X0,X2 : X0] : ((((ord_less_eq @ X0 @ X1 @ X2)) = $true) => ((X1 != X2) => (((ord_less @ X0 @ X1 @ X2)) = $true))))),
% 9.09/1.79 inference(fool_elimination,[],[f506])).
% 9.09/1.79 thf(f778,plain,(
% 9.09/1.79 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => (order @ X0 @ type2 @ X0))),
% 9.09/1.79 inference(rectify,[],[f259])).
% 9.09/1.79 thf(f779,plain,(
% 9.09/1.79 ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0)) = $true) => (((order @ X0 @ type2 @ X0)) = $true))),
% 9.09/1.79 inference(fool_elimination,[],[f778])).
% 9.09/1.79 thf(f820,plain,(
% 9.09/1.79 (linorder @ a @ type2 @ a)),
% 9.09/1.79 inference(rectify,[],[f280])).
% 9.09/1.79 thf(f821,plain,(
% 9.09/1.79 (((linorder @ a @ type2 @ a)) = $true)),
% 9.09/1.79 inference(fool_elimination,[],[f820])).
% 9.09/1.79 thf(f824,plain,(
% 9.09/1.79 ! [X0 : a] : ((member2 @ a @ X0 @ (set2 @ a @ xsa)) => (ord_less_eq @ a @ a2 @ X0)) & (linorder_sorted @ a @ xsa)),
% 9.09/1.79 inference(rectify,[],[f282])).
% 9.09/1.79 thf(f825,plain,(
% 9.09/1.79 ! [X0 : a] : ((((member2 @ a @ X0 @ (set2 @ a @ xsa))) = $true) => (((ord_less_eq @ a @ a2 @ X0)) = $true)) & (((linorder_sorted @ a @ xsa)) = $true)),
% 9.09/1.79 inference(fool_elimination,[],[f824])).
% 9.09/1.79 thf(f826,plain,(
% 9.09/1.79 (distinct @ a @ xsa) & ~(member2 @ a @ a2 @ (set2 @ a @ xsa))),
% 9.09/1.79 inference(rectify,[],[f283])).
% 9.09/1.79 thf(f827,plain,(
% 9.09/1.79 (((distinct @ a @ xsa)) = $true) & ~ (((member2 @ a @ a2 @ (set2 @ a @ xsa))) = $true)),
% 9.09/1.79 inference(fool_elimination,[],[f826])).
% 9.09/1.79 thf(f828,plain,(
% 9.09/1.79 ~((((! [X0 : a] : ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2) = (X0 != x) & ((member2 @ a @ X0 @ (set2 @ a @ xsa)) | (X0 = a2))) | (ord_less @ a @ a2 @ x)) & (! [X1 : a] : (((x != X1) & (member2 @ a @ X1 @ (set2 @ a @ xsa))) | (a2 = X1) = (x != X1) & ((member2 @ a @ X1 @ (set2 @ a @ xsa)) | (a2 = X1))) | ~(ord_less @ a @ a2 @ x))) | (x = a2)) & (! [X2 : a] : (((member2 @ a @ X2 @ (set2 @ a @ xsa))) = (a2 != X2) & ((member2 @ a @ X2 @ (set2 @ a @ xsa)) | (a2 = X2))) | (x != a2)))),
% 9.09/1.79 inference(rectify,[],[f285])).
% 9.09/1.79 thf(f829,plain,(
% 9.09/1.79 ~((((! [X0 : a] : ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa)))) = ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa))) & (~ (x = X0))))) | (((ord_less @ a @ a2 @ x)) = $true)) & (! [X1 : a] : ((((a2 = X1) | ((member2 @ a @ X1 @ (set2 @ a @ xsa)) & (~ (x = X1))))) = ((((a2 = X1) | (member2 @ a @ X1 @ (set2 @ a @ xsa))) & (~ (x = X1))))) | ~ (((ord_less @ a @ a2 @ x)) = $true))) | (x = a2)) & (! [X2 : a] : (((member2 @ a @ X2 @ (set2 @ a @ xsa))) = ((((a2 = X2) | (member2 @ a @ X2 @ (set2 @ a @ xsa))) & (~ (a2 = X2))))) | (x != a2)))),
% 9.09/1.79 inference(fool_elimination,[],[f828])).
% 9.09/1.79 thf(f862,plain,(
% 9.09/1.79 (((distinct @ a @ xsa)) = $true) & (((member2 @ a @ a2 @ (set2 @ a @ xsa))) != $true)),
% 9.09/1.79 inference(flattening,[],[f827])).
% 9.09/1.79 thf(f863,plain,(
% 9.09/1.79 ~((((! [X0 : a] : ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa)))) = ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa))) & (~ (x = X0))))) | (((ord_less @ a @ a2 @ x)) = $true)) & (! [X1 : a] : ((((a2 = X1) | ((member2 @ a @ X1 @ (set2 @ a @ xsa)) & (~ (x = X1))))) = ((((a2 = X1) | (member2 @ a @ X1 @ (set2 @ a @ xsa))) & (~ (x = X1))))) | (((ord_less @ a @ a2 @ x)) != $true))) | (x = a2)) & (! [X2 : a] : (((member2 @ a @ X2 @ (set2 @ a @ xsa))) = ((((a2 = X2) | (member2 @ a @ X2 @ (set2 @ a @ xsa))) & (~ (a2 = X2))))) | (x != a2)))),
% 9.09/1.79 inference(flattening,[],[f829])).
% 9.09/1.79 thf(f1018,plain,(
% 9.09/1.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((((ord_less @ X0 @ X1 @ X2)) = $true) | (X1 = X2)) | (((ord_less_eq @ X0 @ X1 @ X2)) != $true)) | (((order @ X0 @ type2 @ X0)) != $true))),
% 9.09/1.79 inference(ennf_transformation,[],[f507])).
% 9.09/1.79 thf(f1019,plain,(
% 9.09/1.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((((ord_less @ X0 @ X1 @ X2)) = $true) | (X1 = X2) | (((ord_less_eq @ X0 @ X1 @ X2)) != $true)) | (((order @ X0 @ type2 @ X0)) != $true))),
% 9.09/1.79 inference(flattening,[],[f1018])).
% 9.09/1.79 thf(f1173,plain,(
% 9.09/1.79 ! [X0 : $tType] : ((((order @ X0 @ type2 @ X0)) = $true) | (((linorder @ X0 @ type2 @ X0)) != $true))),
% 9.09/1.79 inference(ennf_transformation,[],[f779])).
% 9.09/1.79 thf(f1183,plain,(
% 9.09/1.79 ! [X0 : a] : ((((ord_less_eq @ a @ a2 @ X0)) = $true) | (((member2 @ a @ X0 @ (set2 @ a @ xsa))) != $true)) & (((linorder_sorted @ a @ xsa)) = $true)),
% 9.09/1.79 inference(ennf_transformation,[],[f825])).
% 9.09/1.79 thf(f1184,plain,(
% 9.09/1.79 (((? [X0 : a] : ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa)))) != ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa))) & (~ (x = X0))))) & (((ord_less @ a @ a2 @ x)) != $true)) | (? [X1 : a] : ((((a2 = X1) | ((member2 @ a @ X1 @ (set2 @ a @ xsa)) & (~ (x = X1))))) != ((((a2 = X1) | (member2 @ a @ X1 @ (set2 @ a @ xsa))) & (~ (x = X1))))) & (((ord_less @ a @ a2 @ x)) = $true))) & (x != a2)) | (? [X2 : a] : (((member2 @ a @ X2 @ (set2 @ a @ xsa))) != ((((a2 = X2) | (member2 @ a @ X2 @ (set2 @ a @ xsa))) & (~ (a2 = X2))))) & (x = a2))),
% 9.09/1.79 inference(ennf_transformation,[],[f863])).
% 9.09/1.79 thf(f1222,definition,(
% 9.09/1.79 (? [X1 : a] : ((((a2 = X1) | ((member2 @ a @ X1 @ (set2 @ a @ xsa)) & (~ (x = X1))))) != ((((a2 = X1) | (member2 @ a @ X1 @ (set2 @ a @ xsa))) & (~ (x = X1))))) & (((ord_less @ a @ a2 @ x)) = $true)) | ~ ($true = sP21)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 9.09/1.79 thf(f1223,definition,(
% 9.09/1.79 (? [X0 : a] : ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa)))) != ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa))) & (~ (x = X0))))) & (((ord_less @ a @ a2 @ x)) != $true)) | ($true = sP21) | ~ ($true = sP22)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 9.09/1.79 thf(f1224,definition,(
% 9.09/1.79 (? [X2 : a] : (((member2 @ a @ X2 @ (set2 @ a @ xsa))) != ((((a2 = X2) | (member2 @ a @ X2 @ (set2 @ a @ xsa))) & (~ (a2 = X2))))) & (x = a2)) | ~ ($true = sP23)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 9.09/1.79 thf(f1225,plain,(
% 9.09/1.79 (($true = sP22) & (x != a2)) | ($true = sP23)),
% 9.09/1.79 inference(definition_folding,[],[f1184,f1224,f1223,f1222])).
% 9.09/1.79 thf(f1335,plain,(
% 9.09/1.79 (? [X2 : a] : (((member2 @ a @ X2 @ (set2 @ a @ xsa))) != ((((a2 = X2) | (member2 @ a @ X2 @ (set2 @ a @ xsa))) & (~ (a2 = X2))))) & (x = a2)) | ($true != sP23)),
% 9.09/1.79 inference(nnf_transformation,[],[f1224])).
% 9.09/1.79 thf(f1336,plain,(
% 9.09/1.79 (? [X0 : a] : (((member2 @ a @ X0 @ (set2 @ a @ xsa))) != ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa))) & (~ (a2 = X0))))) & (x = a2)) | ($true != sP23)),
% 9.09/1.79 inference(rectify,[],[f1335])).
% 9.09/1.79 thf(f1337,plain,(
% 9.09/1.79 ((((member2 @ a @ sK111 @ (set2 @ a @ xsa))) != ((((a2 = sK111) | (member2 @ a @ sK111 @ (set2 @ a @ xsa))) & (~ (a2 = sK111))))) & (x = a2)) | ($true != sP23)),
% 9.09/1.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(X0,sK111)],[f1336])).
% 9.09/1.79 thf(f1338,plain,(
% 9.09/1.79 (? [X0 : a] : ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa)))) != ((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa))) & (~ (x = X0))))) & (((ord_less @ a @ a2 @ x)) != $true)) | ($true = sP21) | ($true != sP22)),
% 9.09/1.79 inference(nnf_transformation,[],[f1223])).
% 9.09/1.79 thf(f1339,plain,(
% 9.09/1.79 (((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) != ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))) & (~ (x = sK112))))) & (((ord_less @ a @ a2 @ x)) != $true)) | ($true = sP21) | ($true != sP22)),
% 9.09/1.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(X0,sK112)],[f1338])).
% 9.09/1.79 thf(f1340,plain,(
% 9.09/1.79 (? [X1 : a] : ((((a2 = X1) | ((member2 @ a @ X1 @ (set2 @ a @ xsa)) & (~ (x = X1))))) != ((((a2 = X1) | (member2 @ a @ X1 @ (set2 @ a @ xsa))) & (~ (x = X1))))) & (((ord_less @ a @ a2 @ x)) = $true)) | ($true != sP21)),
% 9.09/1.79 inference(nnf_transformation,[],[f1222])).
% 9.09/1.79 thf(f1341,plain,(
% 9.09/1.79 (? [X0 : a] : (((((a2 = X0) | (member2 @ a @ X0 @ (set2 @ a @ xsa))) & (~ (x = X0)))) != (((a2 = X0) | ((member2 @ a @ X0 @ (set2 @ a @ xsa)) & (~ (x = X0)))))) & (((ord_less @ a @ a2 @ x)) = $true)) | ($true != sP21)),
% 9.09/1.79 inference(rectify,[],[f1340])).
% 9.09/1.79 thf(f1342,plain,(
% 9.09/1.79 ((((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa))) & (~ (x = sK113)))) != (((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113)))))) & (((ord_less @ a @ a2 @ x)) = $true)) | ($true != sP21)),
% 9.09/1.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(X0,sK113)],[f1341])).
% 9.09/1.79 thf(f1502,plain,(
% 9.09/1.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((ord_less_eq @ X0 @ X1 @ X2)) != $true) | (X1 = X2) | (((ord_less @ X0 @ X1 @ X2)) = $true) | (((order @ X0 @ type2 @ X0)) != $true)) )),
% 9.09/1.79 inference(cnf_transformation,[],[f1019])).
% 9.09/1.79 thf(f1689,plain,(
% 9.09/1.79 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0)) != $true) | (((order @ X0 @ type2 @ X0)) = $true)) )),
% 9.09/1.79 inference(cnf_transformation,[],[f1173])).
% 9.09/1.79 thf(f1710,plain,(
% 9.09/1.79 (((linorder @ a @ type2 @ a)) = $true)),
% 9.09/1.79 inference(cnf_transformation,[],[f821])).
% 9.09/1.79 thf(f1715,plain,(
% 9.09/1.79 ( ! [X0 : a] : ((((member2 @ a @ X0 @ (set2 @ a @ xsa))) != $true) | (((ord_less_eq @ a @ a2 @ X0)) = $true)) )),
% 9.09/1.79 inference(cnf_transformation,[],[f1183])).
% 9.09/1.79 thf(f1716,plain,(
% 9.09/1.79 (((member2 @ a @ a2 @ (set2 @ a @ xsa))) != $true)),
% 9.09/1.79 inference(cnf_transformation,[],[f862])).
% 9.09/1.79 thf(f1719,plain,(
% 9.09/1.79 (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) != ((((a2 = sK111) | (member2 @ a @ sK111 @ (set2 @ a @ xsa))) & (~ (a2 = sK111))))) | ($true != sP23)),
% 9.09/1.79 inference(cnf_transformation,[],[f1337])).
% 9.09/1.79 thf(f1720,plain,(
% 9.09/1.79 (((ord_less @ a @ a2 @ x)) != $true) | ($true = sP21) | ($true != sP22)),
% 9.09/1.79 inference(cnf_transformation,[],[f1339])).
% 9.09/1.79 thf(f1721,plain,(
% 9.09/1.79 ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) != ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))) & (~ (x = sK112))))) | ($true = sP21) | ($true != sP22)),
% 9.09/1.79 inference(cnf_transformation,[],[f1339])).
% 9.09/1.79 thf(f1723,plain,(
% 9.09/1.79 (((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa))) & (~ (x = sK113)))) != (((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113)))))) | ($true != sP21)),
% 9.09/1.79 inference(cnf_transformation,[],[f1342])).
% 9.09/1.79 thf(f1724,plain,(
% 9.09/1.79 (x != a2) | ($true = sP23)),
% 9.09/1.79 inference(cnf_transformation,[],[f1225])).
% 9.09/1.79 thf(f1725,plain,(
% 9.09/1.79 ($true = sP22) | ($true = sP23)),
% 9.09/1.79 inference(cnf_transformation,[],[f1225])).
% 9.09/1.79 thf(f1727,definition,(
% 9.09/1.79 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 9.09/1.79 introduced(theory,[fool_exhaustiveness_axiom])).
% 9.09/1.79 thf(f1757,plain,(
% 9.09/1.79 ($true = ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa))) & (~ (x = sK113))))) | ($true != sP21) | ($true = (((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))))),
% 9.09/1.79 inference(xor_proxy_clausification,[],[f1723])).
% 9.09/1.79 thf(f1758,plain,(
% 9.09/1.79 (((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa))) & (~ (x = sK113)))) = $false) | ($true != sP21) | ((((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))) = $false)),
% 9.09/1.79 inference(xor_proxy_clausification,[],[f1723])).
% 9.09/1.79 thf(f1759,plain,(
% 9.09/1.79 (((~ (x = sK113))) = $false) | ($true != sP21) | ((((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))) = $false) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1758])).
% 9.09/1.79 thf(f1760,plain,(
% 9.09/1.79 ($true = ((x = sK113))) | ($true != sP21) | ((((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))) = $false) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(not_proxy_clausification,[],[f1759])).
% 9.09/1.79 thf(f1761,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | ((((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))) = $false) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1760])).
% 9.09/1.79 thf(f1762,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | ((((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113)))) = $false) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1761])).
% 9.09/1.79 thf(f1763,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (((a2 = sK113)) = $false) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1761])).
% 9.09/1.79 thf(f1764,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (a2 != sK113) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1763])).
% 9.09/1.79 thf(f1766,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (a2 != sK113) | (((a2 = sK113)) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1764])).
% 9.09/1.79 thf(f1767,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (a2 != sK113) | (a2 != sK113)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1766])).
% 9.09/1.79 thf(f1768,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (a2 != sK113)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1767])).
% 9.09/1.79 thf(f1769,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (((~ (x = sK113))) = $false) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false) | (((member2 @ a @ sK113 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1762])).
% 9.09/1.79 thf(f1770,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | ($true = ((x = sK113))) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false) | (((member2 @ a @ sK113 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(not_proxy_clausification,[],[f1769])).
% 9.09/1.79 thf(f1771,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (x = sK113) | ((((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa)))) = $false) | (((member2 @ a @ sK113 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1770])).
% 9.09/1.79 thf(f1772,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (x = sK113) | (((member2 @ a @ sK113 @ (set2 @ a @ xsa))) = $false) | (((member2 @ a @ sK113 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1771])).
% 9.09/1.79 thf(f1776,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (((member2 @ a @ sK113 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1772])).
% 9.09/1.79 thf(f1777,plain,(
% 9.09/1.79 ($true = ((~ (x = sK113)))) | ($true != sP21) | ($true = (((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))))),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1757])).
% 9.09/1.79 thf(f1778,plain,(
% 9.09/1.79 ($true = (((a2 = sK113) | (member2 @ a @ sK113 @ (set2 @ a @ xsa))))) | ($true != sP21) | ($true = (((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))))),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1757])).
% 9.09/1.79 thf(f1779,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | ($true != sP21) | ($true = (((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113)))))) | ($true = ((a2 = sK113)))),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1778])).
% 9.09/1.79 thf(f1780,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | ($true != sP21) | ($true = (((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))) | ($true = ((a2 = sK113))) | ($true = ((a2 = sK113)))),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1779])).
% 9.09/1.79 thf(f1782,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | ($true != sP21) | ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | ($true = ((a2 = sK113))) | ($true = ((a2 = sK113)))),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1780])).
% 9.09/1.79 thf(f1783,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | ($true != sP21) | ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | (a2 = sK113) | (a2 = sK113)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1782])).
% 9.09/1.79 thf(f1784,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | ($true != sP21) | (a2 = sK113)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1783])).
% 9.09/1.79 thf(f1789,plain,(
% 9.09/1.79 (((x = sK113)) = $false) | ($true != sP21) | ($true = (((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))))),
% 9.09/1.79 inference(not_proxy_clausification,[],[f1777])).
% 9.09/1.79 thf(f1790,plain,(
% 9.09/1.79 (x != sK113) | ($true != sP21) | ($true = (((a2 = sK113) | ((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))))),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1789])).
% 9.09/1.79 thf(f1791,plain,(
% 9.09/1.79 (x != sK113) | ($true != sP21) | ($true = (((member2 @ a @ sK113 @ (set2 @ a @ xsa)) & (~ (x = sK113))))) | ($true = ((a2 = sK113)))),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1790])).
% 9.09/1.79 thf(f1792,plain,(
% 9.09/1.79 (x != sK113) | ($true != sP21) | ($true = ((~ (x = sK113)))) | ($true = ((a2 = sK113)))),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1791])).
% 9.09/1.79 thf(f1795,plain,(
% 9.09/1.79 (x != sK113) | ($true != sP21) | (((x = sK113)) = $false) | ($true = ((a2 = sK113)))),
% 9.09/1.79 inference(not_proxy_clausification,[],[f1792])).
% 9.09/1.79 thf(f1796,plain,(
% 9.09/1.79 (x != sK113) | ($true != sP21) | (x != sK113) | ($true = ((a2 = sK113)))),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1795])).
% 9.09/1.79 thf(f1797,plain,(
% 9.09/1.79 (x != sK113) | ($true != sP21) | (x != sK113) | (a2 = sK113)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1796])).
% 9.09/1.79 thf(f1798,plain,(
% 9.09/1.79 (x != sK113) | ($true != sP21) | (a2 = sK113)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1797])).
% 9.09/1.79 thf(f1799,plain,(
% 9.09/1.79 ($true = (((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))))) | ($true = sP21) | ($true != sP22) | ($true = ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))) & (~ (x = sK112)))))),
% 9.09/1.79 inference(xor_proxy_clausification,[],[f1721])).
% 9.09/1.79 thf(f1800,plain,(
% 9.09/1.79 ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) = $false) | ($true = sP21) | ($true != sP22) | (((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))) & (~ (x = sK112)))) = $false)),
% 9.09/1.79 inference(xor_proxy_clausification,[],[f1721])).
% 9.09/1.79 thf(f1801,plain,(
% 9.09/1.79 (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false) | ($true = sP21) | ($true != sP22) | (((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))) & (~ (x = sK112)))) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1800])).
% 9.09/1.79 thf(f1802,plain,(
% 9.09/1.79 (((a2 = sK112)) = $false) | ($true = sP21) | ($true != sP22) | (((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))) & (~ (x = sK112)))) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1800])).
% 9.09/1.79 thf(f1803,plain,(
% 9.09/1.79 (a2 != sK112) | ($true = sP21) | ($true != sP22) | (((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))) & (~ (x = sK112)))) = $false)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1802])).
% 9.09/1.79 thf(f1804,plain,(
% 9.09/1.79 (a2 != sK112) | ($true = sP21) | ($true != sP22) | (((~ (x = sK112))) = $false) | ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1803])).
% 9.09/1.79 thf(f1805,plain,(
% 9.09/1.79 (a2 != sK112) | ($true = sP21) | ($true != sP22) | ($true = ((x = sK112))) | ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(not_proxy_clausification,[],[f1804])).
% 9.09/1.79 thf(f1806,plain,(
% 9.09/1.79 (a2 != sK112) | ($true = sP21) | ($true != sP22) | (x = sK112) | ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1805])).
% 9.09/1.79 thf(f1808,plain,(
% 9.09/1.79 (a2 != sK112) | ($true = sP21) | ($true != sP22) | (x = sK112) | (((a2 = sK112)) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1806])).
% 9.09/1.79 thf(f1809,plain,(
% 9.09/1.79 (a2 != sK112) | ($true = sP21) | ($true != sP22) | (x = sK112) | (a2 != sK112)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1808])).
% 9.09/1.79 thf(f1810,plain,(
% 9.09/1.79 (a2 != sK112) | ($true = sP21) | ($true != sP22) | (x = sK112)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1809])).
% 9.09/1.79 thf(f1811,plain,(
% 9.09/1.79 (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false) | ($true = sP21) | ($true != sP22) | (((~ (x = sK112))) = $false) | ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1801])).
% 9.09/1.79 thf(f1812,plain,(
% 9.09/1.79 (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false) | ($true = sP21) | ($true != sP22) | ($true = ((x = sK112))) | ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(not_proxy_clausification,[],[f1811])).
% 9.09/1.79 thf(f1813,plain,(
% 9.09/1.79 (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false) | ($true = sP21) | ($true != sP22) | (x = sK112) | ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1812])).
% 9.09/1.79 thf(f1814,plain,(
% 9.09/1.79 (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false) | ($true = sP21) | ($true != sP22) | (x = sK112) | (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1813])).
% 9.09/1.79 thf(f1817,plain,(
% 9.09/1.79 (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false) | ($true = sP21) | ($true != sP22) | (x = sK112)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1814])).
% 9.09/1.79 thf(f1818,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | ($true = sP21) | ($true != sP22) | ($true = ((((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))) & (~ (x = sK112))))) | ($true = ((a2 = sK112)))),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1799])).
% 9.09/1.79 thf(f1820,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | ($true = sP21) | ($true != sP22) | ($true = (((a2 = sK112) | (member2 @ a @ sK112 @ (set2 @ a @ xsa))))) | ($true = ((a2 = sK112)))),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1818])).
% 9.09/1.79 thf(f1821,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | ($true = sP21) | ($true != sP22) | ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | ($true = ((a2 = sK112))) | ($true = ((a2 = sK112)))),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1820])).
% 9.09/1.79 thf(f1822,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | ($true = sP21) | ($true != sP22) | ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | (a2 = sK112) | (a2 = sK112)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1821])).
% 9.09/1.79 thf(f1823,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | ($true = sP21) | ($true != sP22) | (a2 = sK112)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1822])).
% 9.09/1.79 thf(f1827,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true != sP23) | ($true = ((((a2 = sK111) | (member2 @ a @ sK111 @ (set2 @ a @ xsa))) & (~ (a2 = sK111)))))),
% 9.09/1.79 inference(xor_proxy_clausification,[],[f1719])).
% 9.09/1.79 thf(f1828,plain,(
% 9.09/1.79 (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false) | ($true != sP23) | (((((a2 = sK111) | (member2 @ a @ sK111 @ (set2 @ a @ xsa))) & (~ (a2 = sK111)))) = $false)),
% 9.09/1.79 inference(xor_proxy_clausification,[],[f1719])).
% 9.09/1.79 thf(f1829,plain,(
% 9.09/1.79 (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false) | ($true != sP23) | (((~ (a2 = sK111))) = $false) | ((((a2 = sK111) | (member2 @ a @ sK111 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1828])).
% 9.09/1.79 thf(f1830,plain,(
% 9.09/1.79 (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false) | ($true != sP23) | ($true = ((a2 = sK111))) | ((((a2 = sK111) | (member2 @ a @ sK111 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(not_proxy_clausification,[],[f1829])).
% 9.09/1.79 thf(f1831,plain,(
% 9.09/1.79 (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false) | ($true != sP23) | (a2 = sK111) | ((((a2 = sK111) | (member2 @ a @ sK111 @ (set2 @ a @ xsa)))) = $false)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1830])).
% 9.09/1.79 thf(f1832,plain,(
% 9.09/1.79 (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false) | ($true != sP23) | (a2 = sK111) | (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1831])).
% 9.09/1.79 thf(f1835,plain,(
% 9.09/1.79 (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false) | ($true != sP23) | (a2 = sK111)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1832])).
% 9.09/1.79 thf(f1836,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true != sP23) | ($true = ((~ (a2 = sK111))))),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1827])).
% 9.09/1.79 thf(f1837,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true != sP23) | ($true = (((a2 = sK111) | (member2 @ a @ sK111 @ (set2 @ a @ xsa)))))),
% 9.09/1.79 inference(and_proxy_clausification,[],[f1827])).
% 9.09/1.79 thf(f1838,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true != sP23) | ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true = ((a2 = sK111)))),
% 9.09/1.79 inference(or_proxy_clausification,[],[f1837])).
% 9.09/1.79 thf(f1839,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true != sP23) | ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | (a2 = sK111)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1838])).
% 9.09/1.79 thf(f1840,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true != sP23) | (a2 = sK111)),
% 9.09/1.79 inference(duplicate_literal_removal,[],[f1839])).
% 9.09/1.79 thf(f1841,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true != sP23) | (((a2 = sK111)) = $false)),
% 9.09/1.79 inference(not_proxy_clausification,[],[f1836])).
% 9.09/1.79 thf(f1842,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ($true != sP23) | (a2 != sK111)),
% 9.09/1.79 inference(equality_proxy_clausification,[],[f1841])).
% 9.09/1.79 thf(f2173,definition,(
% 9.09/1.79 spl124_1 <=> ($true = sP23)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_1])],[avatar_definition])).
% 9.09/1.79 thf(f2177,definition,(
% 9.09/1.79 spl124_2 <=> (x = a2)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_2])],[avatar_definition])).
% 9.09/1.79 thf(f2180,plain,(
% 9.09/1.79 spl124_1 | ~spl124_2),
% 9.09/1.79 inference(avatar_split_clause,[],[f1724,f2177,f2173])).
% 9.09/1.79 thf(f2182,definition,(
% 9.09/1.79 spl124_3 <=> ($true = sP22)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_3])],[avatar_definition])).
% 9.09/1.79 thf(f2185,plain,(
% 9.09/1.79 spl124_1 | spl124_3),
% 9.09/1.79 inference(avatar_split_clause,[],[f1725,f2182,f2173])).
% 9.09/1.79 thf(f2187,definition,(
% 9.09/1.79 spl124_4 <=> ($true = sP21)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_4])],[avatar_definition])).
% 9.09/1.79 thf(f2191,definition,(
% 9.09/1.79 spl124_5 <=> (((ord_less @ a @ a2 @ x)) = $true)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_5])],[avatar_definition])).
% 9.09/1.79 thf(f2192,plain,(
% 9.09/1.79 (((ord_less @ a @ a2 @ x)) != $true) | spl124_5),
% 9.09/1.79 inference(avatar_component_clause,[],[f2191])).
% 9.09/1.79 thf(f2196,definition,(
% 9.09/1.79 spl124_6 <=> (a2 = sK113)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_6])],[avatar_definition])).
% 9.09/1.79 thf(f2197,plain,(
% 9.09/1.79 (a2 = sK113) | ~spl124_6),
% 9.09/1.79 inference(avatar_component_clause,[],[f2196])).
% 9.09/1.79 thf(f2200,definition,(
% 9.09/1.79 spl124_7 <=> (x = sK113)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_7])],[avatar_definition])).
% 9.09/1.79 thf(f2202,plain,(
% 9.09/1.79 (x = sK113) | ~spl124_7),
% 9.09/1.79 inference(avatar_component_clause,[],[f2200])).
% 9.09/1.79 thf(f2204,plain,(
% 9.09/1.79 (x = sK113) | ($true != sP21) | (a2 != sK113)),
% 9.09/1.79 inference(global_subsumption,[],[f1768])).
% 9.09/1.79 thf(f2206,definition,(
% 9.09/1.79 spl124_8 <=> (((member2 @ a @ sK113 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_8])],[avatar_definition])).
% 9.09/1.79 thf(f2208,plain,(
% 9.09/1.79 (((member2 @ a @ sK113 @ (set2 @ a @ xsa))) = $false) | ~spl124_8),
% 9.09/1.79 inference(avatar_component_clause,[],[f2206])).
% 9.09/1.79 thf(f2210,plain,(
% 9.09/1.79 spl124_8 | ~spl124_4 | spl124_7),
% 9.09/1.79 inference(avatar_split_clause,[],[f1776,f2200,f2187,f2206])).
% 9.09/1.79 thf(f2212,definition,(
% 9.09/1.79 spl124_9 <=> ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa))))),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_9])],[avatar_definition])).
% 9.09/1.79 thf(f2214,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | ~spl124_9),
% 9.09/1.79 inference(avatar_component_clause,[],[f2212])).
% 9.09/1.79 thf(f2217,plain,(
% 9.09/1.79 ($true != sP21) | ($true = ((member2 @ a @ sK113 @ (set2 @ a @ xsa)))) | (a2 = sK113)),
% 9.09/1.79 inference(global_subsumption,[],[f1784])).
% 9.09/1.79 thf(f2218,plain,(
% 9.09/1.79 spl124_6 | ~spl124_4 | ~spl124_7),
% 9.09/1.79 inference(avatar_split_clause,[],[f1798,f2200,f2187,f2196])).
% 9.09/1.79 thf(f2219,plain,(
% 9.09/1.79 ~spl124_3 | spl124_4 | ~spl124_5),
% 9.09/1.79 inference(avatar_split_clause,[],[f1720,f2191,f2187,f2182])).
% 9.09/1.79 thf(f2221,definition,(
% 9.09/1.79 spl124_10 <=> (x = sK112)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_10])],[avatar_definition])).
% 9.09/1.79 thf(f2223,plain,(
% 9.09/1.79 (x = sK112) | ~spl124_10),
% 9.09/1.79 inference(avatar_component_clause,[],[f2221])).
% 9.09/1.79 thf(f2225,definition,(
% 9.09/1.79 spl124_11 <=> (a2 = sK112)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_11])],[avatar_definition])).
% 9.09/1.79 thf(f2226,plain,(
% 9.09/1.79 (a2 = sK112) | ~spl124_11),
% 9.09/1.79 inference(avatar_component_clause,[],[f2225])).
% 9.09/1.79 thf(f2228,plain,(
% 9.09/1.79 spl124_10 | ~spl124_3 | spl124_4 | ~spl124_11),
% 9.09/1.79 inference(avatar_split_clause,[],[f1810,f2225,f2187,f2182,f2221])).
% 9.09/1.79 thf(f2232,definition,(
% 9.09/1.79 spl124_12 <=> (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_12])],[avatar_definition])).
% 9.09/1.79 thf(f2234,plain,(
% 9.09/1.79 (((member2 @ a @ sK112 @ (set2 @ a @ xsa))) = $false) | ~spl124_12),
% 9.09/1.79 inference(avatar_component_clause,[],[f2232])).
% 9.09/1.79 thf(f2235,plain,(
% 9.09/1.79 spl124_10 | ~spl124_3 | spl124_4 | spl124_12),
% 9.09/1.79 inference(avatar_split_clause,[],[f1817,f2232,f2187,f2182,f2221])).
% 9.09/1.79 thf(f2237,definition,(
% 9.09/1.79 spl124_13 <=> ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa))))),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_13])],[avatar_definition])).
% 9.09/1.79 thf(f2239,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | ~spl124_13),
% 9.09/1.79 inference(avatar_component_clause,[],[f2237])).
% 9.09/1.79 thf(f2241,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK112 @ (set2 @ a @ xsa)))) | ($true = sP21) | ($true != sP22) | (a2 = sK112)),
% 9.09/1.79 inference(global_subsumption,[],[f1823])).
% 9.09/1.79 thf(f2244,definition,(
% 9.09/1.79 spl124_14 <=> (a2 = sK111)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_14])],[avatar_definition])).
% 9.09/1.79 thf(f2246,plain,(
% 9.09/1.79 (a2 = sK111) | ~spl124_14),
% 9.09/1.79 inference(avatar_component_clause,[],[f2244])).
% 9.09/1.79 thf(f2248,definition,(
% 9.09/1.79 spl124_15 <=> (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_15])],[avatar_definition])).
% 9.09/1.79 thf(f2250,plain,(
% 9.09/1.79 (((member2 @ a @ sK111 @ (set2 @ a @ xsa))) = $false) | ~spl124_15),
% 9.09/1.79 inference(avatar_component_clause,[],[f2248])).
% 9.09/1.79 thf(f2251,plain,(
% 9.09/1.79 spl124_14 | ~spl124_1 | spl124_15),
% 9.09/1.79 inference(avatar_split_clause,[],[f1835,f2248,f2173,f2244])).
% 9.09/1.79 thf(f2253,definition,(
% 9.09/1.79 spl124_16 <=> ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa))))),
% 9.09/1.79 introduced(definition,[new_symbols(definition,[spl124_16])],[avatar_definition])).
% 9.09/1.79 thf(f2255,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ sK111 @ (set2 @ a @ xsa)))) | ~spl124_16),
% 9.09/1.79 inference(avatar_component_clause,[],[f2253])).
% 9.09/1.79 thf(f2256,plain,(
% 9.09/1.79 spl124_14 | ~spl124_1 | spl124_16),
% 9.09/1.79 inference(avatar_split_clause,[],[f1840,f2253,f2173,f2244])).
% 9.09/1.79 thf(f2257,plain,(
% 9.09/1.79 ~spl124_14 | ~spl124_1 | spl124_16),
% 9.09/1.79 inference(avatar_split_clause,[],[f1842,f2253,f2173,f2244])).
% 9.09/1.79 thf(f2259,plain,(
% 9.09/1.79 ~spl124_6 | ~spl124_4 | spl124_7),
% 9.09/1.79 inference(avatar_split_clause,[],[f2204,f2200,f2187,f2196])).
% 9.09/1.79 thf(f2261,plain,(
% 9.09/1.79 spl124_6 | spl124_9 | ~spl124_4),
% 9.09/1.79 inference(avatar_split_clause,[],[f2217,f2187,f2212,f2196])).
% 9.09/1.79 thf(f2264,plain,(
% 9.09/1.79 spl124_11 | ~spl124_3 | spl124_4 | spl124_13),
% 9.09/1.79 inference(avatar_split_clause,[],[f2241,f2237,f2187,f2182,f2225])).
% 9.09/1.79 thf(f2265,plain,(
% 9.09/1.79 (x = a2) | (~spl124_6 | ~spl124_7)),
% 9.09/1.79 inference(forward_demodulation,[],[f2202,f2197])).
% 9.09/1.79 thf(f2266,plain,(
% 9.09/1.79 spl124_2 | ~spl124_6 | ~spl124_7),
% 9.09/1.79 inference(avatar_split_clause,[],[f2265,f2200,f2196,f2177])).
% 9.09/1.79 thf(f2269,plain,(
% 9.09/1.79 (x = a2) | (~spl124_10 | ~spl124_11)),
% 9.09/1.79 inference(constrained_superposition,[],[f2223,f2226])).
% 9.09/1.79 thf(f2270,plain,(
% 9.09/1.79 spl124_2 | ~spl124_10 | ~spl124_11),
% 9.09/1.79 inference(avatar_split_clause,[],[f2269,f2225,f2221,f2177])).
% 9.09/1.79 thf(f2272,plain,(
% 9.09/1.79 ($true = ((member2 @ a @ x @ (set2 @ a @ xsa)))) | (~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(forward_demodulation,[],[f2239,f2223])).
% 9.09/1.79 thf(f2275,plain,(
% 9.09/1.79 ($true != $true) | (((member2 @ a @ a2 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(constrained_superposition,[],[f1716,f1727])).
% 9.09/1.79 thf(f2281,plain,(
% 9.09/1.79 (((member2 @ a @ a2 @ (set2 @ a @ xsa))) = $false)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f2275])).
% 9.09/1.79 thf(f2301,plain,(
% 9.09/1.79 ($true != $true) | ($true = ((order @ a @ type2 @ a)))),
% 9.09/1.79 inference(constrained_superposition,[],[f1689,f1710])).
% 9.09/1.79 thf(f2304,plain,(
% 9.09/1.79 ($true = ((order @ a @ type2 @ a)))),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f2301])).
% 9.09/1.79 thf(f2353,plain,(
% 9.09/1.79 ($true != $true) | (((ord_less @ a @ a2 @ x)) = $false) | spl124_5),
% 9.09/1.79 inference(constrained_superposition,[],[f2192,f1727])).
% 9.09/1.79 thf(f2354,plain,(
% 9.09/1.79 (((ord_less @ a @ a2 @ x)) = $false) | spl124_5),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f2353])).
% 9.09/1.79 thf(f3445,plain,(
% 9.09/1.79 ($true != $true) | ($true = ((ord_less_eq @ a @ a2 @ x))) | (~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(constrained_superposition,[],[f1715,f2272])).
% 9.09/1.79 thf(f3446,plain,(
% 9.09/1.79 ($true = ((ord_less_eq @ a @ a2 @ x))) | (~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f3445])).
% 9.09/1.79 thf(f3472,plain,(
% 9.09/1.79 ($true != $true) | (x = a2) | (((ord_less @ a @ a2 @ x)) = $true) | ($true != ((order @ a @ type2 @ a))) | (~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(constrained_superposition,[],[f1502,f3446])).
% 9.09/1.79 thf(f3486,plain,(
% 9.09/1.79 (x = a2) | (((ord_less @ a @ a2 @ x)) = $true) | ($true != ((order @ a @ type2 @ a))) | (~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f3472])).
% 9.09/1.79 thf(f3516,plain,(
% 9.09/1.79 ($true = $false) | (x = a2) | ($true != ((order @ a @ type2 @ a))) | (spl124_5 | ~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(forward_demodulation,[],[f3486,f2354])).
% 9.09/1.79 thf(f3517,plain,(
% 9.09/1.79 (x = a2) | ($true != ((order @ a @ type2 @ a))) | (spl124_5 | ~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f3516])).
% 9.09/1.79 thf(f3524,plain,(
% 9.09/1.79 ($true != $true) | (x = a2) | (spl124_5 | ~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(forward_demodulation,[],[f3517,f2304])).
% 9.09/1.79 thf(f3525,plain,(
% 9.09/1.79 (x = a2) | (spl124_5 | ~spl124_10 | ~spl124_13)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f3524])).
% 9.09/1.79 thf(f3526,plain,(
% 9.09/1.79 spl124_2 | spl124_5 | ~spl124_10 | ~spl124_13),
% 9.09/1.79 inference(avatar_split_clause,[],[f3525,f2237,f2221,f2191,f2177])).
% 9.09/1.79 thf(f3527,plain,(
% 9.09/1.79 ($true = $false) | (~spl124_12 | ~spl124_13)),
% 9.09/1.79 inference(forward_demodulation,[],[f2239,f2234])).
% 9.09/1.79 thf(f3528,plain,(
% 9.09/1.79 $false | (~spl124_12 | ~spl124_13)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f3527])).
% 9.09/1.79 thf(f3529,plain,(
% 9.09/1.79 ~spl124_12 | ~spl124_13),
% 9.09/1.79 inference(avatar_contradiction_clause,[],[f3528])).
% 9.09/1.79 thf(f3530,plain,(
% 9.09/1.79 ($true = $false) | (~spl124_8 | ~spl124_9)),
% 9.09/1.79 inference(forward_demodulation,[],[f2214,f2208])).
% 9.09/1.79 thf(f3531,plain,(
% 9.09/1.79 $false | (~spl124_8 | ~spl124_9)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f3530])).
% 9.09/1.79 thf(f3532,plain,(
% 9.09/1.79 ~spl124_8 | ~spl124_9),
% 9.09/1.79 inference(avatar_contradiction_clause,[],[f3531])).
% 9.09/1.79 thf(f3535,plain,(
% 9.09/1.79 (((member2 @ a @ a2 @ (set2 @ a @ xsa))) = $true) | (~spl124_14 | ~spl124_16)),
% 9.09/1.79 inference(forward_demodulation,[],[f2255,f2246])).
% 9.09/1.79 thf(f3536,plain,(
% 9.09/1.79 ($true = $false) | (~spl124_14 | ~spl124_16)),
% 9.09/1.79 inference(forward_demodulation,[],[f3535,f2281])).
% 9.09/1.79 thf(f3537,plain,(
% 9.09/1.79 $false | (~spl124_14 | ~spl124_16)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f3536])).
% 9.09/1.79 thf(f3538,plain,(
% 9.09/1.79 ~spl124_14 | ~spl124_16),
% 9.09/1.79 inference(avatar_contradiction_clause,[],[f3537])).
% 9.09/1.79 thf(f3539,plain,(
% 9.09/1.79 ($true = $false) | (~spl124_15 | ~spl124_16)),
% 9.09/1.79 inference(forward_demodulation,[],[f2255,f2250])).
% 9.09/1.79 thf(f3540,plain,(
% 9.09/1.79 $false | (~spl124_15 | ~spl124_16)),
% 9.09/1.79 inference(trivial_inequality_removal,[],[f3539])).
% 9.09/1.79 thf(f3541,plain,(
% 9.09/1.79 ~spl124_15 | ~spl124_16),
% 9.09/1.79 inference(avatar_contradiction_clause,[],[f3540])).
% 9.09/1.79 cnf(s2, plain, spl124_1 | ~spl124_2, inference(sat_conversion,[],[f2180])).
% 9.09/1.79 cnf(s4, plain, spl124_1 | spl124_3, inference(sat_conversion,[],[f2185])).
% 9.09/1.79 cnf(s13, plain, ~spl124_4 | spl124_7 | spl124_8, inference(sat_conversion,[],[f2210])).
% 9.09/1.79 cnf(s19, plain, ~spl124_4 | spl124_6 | ~spl124_7, inference(sat_conversion,[],[f2218])).
% 9.09/1.79 cnf(s21, plain, ~spl124_3 | spl124_4 | ~spl124_5, inference(sat_conversion,[],[f2219])).
% 9.09/1.79 cnf(s23, plain, ~spl124_3 | spl124_4 | spl124_10 | ~spl124_11, inference(sat_conversion,[],[f2228])).
% 9.09/1.79 cnf(s27, plain, ~spl124_3 | spl124_4 | spl124_10 | spl124_12, inference(sat_conversion,[],[f2235])).
% 9.09/1.79 cnf(s34, plain, ~spl124_1 | spl124_14 | spl124_15, inference(sat_conversion,[],[f2251])).
% 9.09/1.79 cnf(s36, plain, ~spl124_1 | spl124_14 | spl124_16, inference(sat_conversion,[],[f2256])).
% 9.09/1.79 cnf(s38, plain, ~spl124_1 | ~spl124_14 | spl124_16, inference(sat_conversion,[],[f2257])).
% 9.09/1.79 cnf(s423, plain, ~spl124_4 | ~spl124_6 | spl124_7, inference(sat_conversion,[],[f2259])).
% 9.09/1.79 cnf(s427, plain, ~spl124_4 | spl124_6 | spl124_9, inference(sat_conversion,[],[f2261])).
% 9.09/1.79 cnf(s433, plain, ~spl124_3 | spl124_4 | spl124_11 | spl124_13, inference(sat_conversion,[],[f2264])).
% 9.09/1.79 cnf(s441, plain, spl124_2 | ~spl124_6 | ~spl124_7, inference(sat_conversion,[],[f2266])).
% 9.09/1.79 cnf(s447, plain, spl124_2 | ~spl124_10 | ~spl124_11, inference(sat_conversion,[],[f2270])).
% 9.09/1.79 cnf(s703, plain, spl124_2 | spl124_5 | ~spl124_10 | ~spl124_13, inference(sat_conversion,[],[f3526])).
% 9.09/1.79 cnf(s707, plain, ~spl124_12 | ~spl124_13, inference(sat_conversion,[],[f3529])).
% 9.09/1.79 cnf(s712, plain, ~spl124_8 | ~spl124_9, inference(sat_conversion,[],[f3532])).
% 9.09/1.79 cnf(s720, plain, ~spl124_14 | ~spl124_16, inference(sat_conversion,[],[f3538])).
% 9.09/1.79 cnf(s723, plain, ~spl124_15 | ~spl124_16, inference(sat_conversion,[],[f3541])).
% 9.09/1.79 cnf(s724, plain, spl124_10 | spl124_4 | ~spl124_3, inference(rat,[],[s433,s707,s23,s27])).
% 9.09/1.79 cnf(s725, plain, spl124_4 | spl124_1, inference(rat,[],[s433,s703,s447,s724,s21,s4,s2])).
% 9.09/1.79 cnf(s726, plain, spl124_6 | ~spl124_4, inference(rat,[],[s13,s712,s19,s427])).
% 9.09/1.79 cnf(s727, plain, spl124_1, inference(rat,[],[s423,s441,s726,s725,s2])).
% 9.09/1.79 cnf(s729, plain, spl124_14, inference(rat,[],[s723,s36,s34,s727])).
% 9.09/1.79 cnf(s730, plain, ~spl124_16, inference(rat,[],[s720,s729])).
% 9.09/1.79 cnf(s731, plain, $false, inference(rat,[],[s38,s727,s730,s729])).
% 9.09/1.79 thf(f3542,plain,(
% 9.09/1.79 $false),
% 9.09/1.79 inference(avatar_sat_refutation,[],[s731])).
% 9.09/1.79 % SZS output end Proof for theBenchmark
% 9.09/1.79 % (2462228)------------------------------
% 9.09/1.79 % (2462228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.09/1.79 % (2462228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.09/1.79 % (2462228)CaDiCaL version: 2.1.3
% 9.09/1.79 % (2462228)Termination reason: Refutation
% 9.09/1.79 % (2462228)Time elapsed: 0.252 s
% 9.09/1.79 % (2462228)Peak memory usage: 16 MB
% 9.09/1.79 % (2462228)Instructions burned: 499 (million)
% 9.09/1.79 % (2462165)Success in time 1.551 s
% 9.09/1.79 % Vampire exiting
%------------------------------------------------------------------------------