%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV492^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:39:35 AM UTC 2026
% Result : Theorem 3.77s 1.03s
% Output : Refutation 3.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV492^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.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 15:54:59 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.77/0.91 % (2668781)Will run a generic schedule for satisfiability detection.
% 3.77/0.91 % (2668787)% WARNING: option uhcvi not known.
% 3.77/0.91 % (2668787)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=344901937:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.77/0.91 % (2668790)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1549492800:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.77/0.91 % (2668788)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=724044407:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.77/0.91 % (2668789)dis+10_1_sil=32000:sp=arity:random_seed=757595260:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.77/0.91 % (2668786)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3843236626_2999 on theBenchmark for (2999ds/0Mi)
% 3.77/0.91 % (2668787)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.91 % (2668790)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.91 % (2668787)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.77/0.91 % Exception at run slice level
% 3.77/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.91 % (2668791)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=598441711:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.77/0.91 % (2668792)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2225235925:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.77/0.91 % (2668798)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4197621420:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.77/0.91 % Exception at run slice level
% 3.77/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.91 % (2668802)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1302358848:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.77/0.91 % (2668789)Instruction limit reached!
% 3.77/0.91 % (2668789)------------------------------
% 3.77/0.91 % (2668789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.91 % (2668789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.91 % (2668789)CaDiCaL version: 2.1.3
% 3.77/0.91 % (2668789)Termination reason: Instruction limit
% 3.77/0.91 % (2668789)Termination phase: Saturation
% 3.77/0.91 % (2668789)Time elapsed: 0.051 s
% 3.77/0.91 % (2668789)Peak memory usage: 12 MB
% 3.77/0.91 % (2668789)Instructions burned: 104 (million)
% 3.77/0.91 % (2668790)Instruction limit reached!
% 3.77/0.91 % (2668790)------------------------------
% 3.77/0.91 % (2668790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.91 % (2668790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.91 % (2668790)CaDiCaL version: 2.1.3
% 3.77/0.91 % (2668790)Termination reason: Instruction limit
% 3.77/0.91 % (2668790)Termination phase: Saturation
% 3.77/0.91 % (2668790)Time elapsed: 0.056 s
% 3.77/0.91 % (2668790)Peak memory usage: 12 MB
% 3.77/0.91 % (2668790)Instructions burned: 117 (million)
% 3.77/0.91 % (2668792)Instruction limit reached!
% 3.77/0.91 % (2668792)------------------------------
% 3.77/0.91 % (2668792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.91 % (2668792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.91 % (2668792)CaDiCaL version: 2.1.3
% 3.77/0.91 % (2668792)Termination reason: Instruction limit
% 3.77/0.91 % (2668792)Termination phase: Saturation
% 3.77/0.91 % (2668792)Time elapsed: 0.062 s
% 3.77/0.91 % (2668792)Peak memory usage: 13 MB
% 3.77/0.91 % (2668792)Instructions burned: 161 (million)
% 3.77/0.91 % (2668804)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=1435806566:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.77/0.91 % (2668804)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.91 % (2668804)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.77/0.91 % (2668805)ott-21_1_sil=16000:fs=off:random_seed=1027250878:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.77/0.91 % (2668791)Instruction limit reached!
% 3.77/1.03 % (2668791)------------------------------
% 3.77/1.03 % (2668791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.03 % (2668791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.03 % (2668791)CaDiCaL version: 2.1.3
% 3.77/1.03 % (2668791)Termination reason: Instruction limit
% 3.77/1.03 % (2668791)Termination phase: Saturation
% 3.77/1.03 % (2668791)Time elapsed: 0.071 s
% 3.77/1.03 % (2668791)Peak memory usage: 12 MB
% 3.77/1.03 % (2668791)Instructions burned: 132 (million)
% 3.77/1.03 % (2668806)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2349064826:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.77/1.03 % (2668809)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1516607757:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.77/1.03 % Exception at run slice level
% 3.77/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/1.03 % (2668802)Instruction limit reached!
% 3.77/1.03 % (2668802)------------------------------
% 3.77/1.03 % (2668802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.03 % (2668802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.03 % (2668802)CaDiCaL version: 2.1.3
% 3.77/1.03 % (2668802)Termination reason: Instruction limit
% 3.77/1.03 % (2668802)Termination phase: Saturation
% 3.77/1.03 % (2668802)Time elapsed: 0.071 s
% 3.77/1.03 % (2668802)Peak memory usage: 12 MB
% 3.77/1.03 % (2668802)Instructions burned: 133 (million)
% 3.77/1.03 % (2668812)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3131818513:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.77/1.03 % (2668813)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=960651104:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.77/1.03 % Exception at run slice level
% 3.77/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/1.03 % (2668816)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=1162019412:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 3.77/1.03 % (2668816)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/1.03 % (2668805)Instruction limit reached!
% 3.77/1.03 % (2668805)------------------------------
% 3.77/1.03 % (2668805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.03 % (2668805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.03 % (2668805)CaDiCaL version: 2.1.3
% 3.77/1.03 % (2668805)Termination reason: Instruction limit
% 3.77/1.03 % (2668805)Termination phase: Saturation
% 3.77/1.03 % (2668805)Time elapsed: 0.082 s
% 3.77/1.03 % (2668805)Peak memory usage: 12 MB
% 3.77/1.03 % (2668805)Instructions burned: 180 (million)
% 3.77/1.03 % (2668818)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1941035996:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 3.77/1.03 % (2668818)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/1.03 % (2668804)Instruction limit reached!
% 3.77/1.03 % (2668804)------------------------------
% 3.77/1.03 % (2668804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.03 % (2668804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.03 % (2668804)CaDiCaL version: 2.1.3
% 3.77/1.03 % (2668804)Termination reason: Instruction limit
% 3.77/1.03 % (2668804)Termination phase: Saturation
% 3.77/1.03 % (2668804)Time elapsed: 0.229 s
% 3.77/1.03 % (2668804)Peak memory usage: 13 MB
% 3.77/1.03 % (2668804)Instructions burned: 685 (million)
% 3.77/1.03 % (2668820)fmb+10_1_sil=64000:random_seed=1826346858:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.77/1.03 % (2668820)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.77/1.03 % Exception at run slice level
% 3.77/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/1.03 % (2668806)Instruction limit reached!
% 3.77/1.03 % (2668806)------------------------------
% 3.77/1.03 % (2668806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.03 % (2668806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.03 % (2668806)CaDiCaL version: 2.1.3
% 3.77/1.03 % (2668806)Termination reason: Instruction limit
% 3.77/1.03 % (2668806)Termination phase: Saturation
% 3.77/1.03 % (2668806)Time elapsed: 0.225 s
% 3.77/1.03 % (2668806)Peak memory usage: 12 MB
% 3.77/1.03 % (2668806)Instructions burned: 479 (million)
% 3.77/1.03 % (2668822)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2966204984:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.77/1.03 % (2668823)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=927237252:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 3.77/1.03 % Exception at run slice level
% 3.77/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/1.03 % Exception at run slice level
% 3.77/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/1.03 % (2668826)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=457555065:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.77/1.03 % (2668826)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/1.03 % (2668827)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=111914172:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 3.77/1.03 % (2668827)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.77/1.03 % (2668827)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.77/1.03 % (2668816)Instruction limit reached!
% 3.77/1.03 % (2668816)------------------------------
% 3.77/1.03 % (2668816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.03 % (2668816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.03 % (2668816)CaDiCaL version: 2.1.3
% 3.77/1.03 % (2668816)Termination reason: Instruction limit
% 3.77/1.03 % (2668816)Termination phase: Saturation
% 3.77/1.03 % (2668816)Time elapsed: 0.235 s
% 3.77/1.03 % (2668816)Peak memory usage: 12 MB
% 3.77/1.03 % (2668816)Instructions burned: 695 (million)
% 3.77/1.03 % (2668830)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1328505347:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 3.77/1.03 % Exception at run slice level
% 3.77/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/1.03 % (2668832)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1063397963:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 3.77/1.03 % Exception at run slice level
% 3.77/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/1.03 % (2668834)ott-2_1_sil=16000:newcnf=on:random_seed=152911442:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 3.77/1.03 % (2668834)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/1.03 % (2668812)Instruction limit reached!
% 3.77/1.03 % (2668812)------------------------------
% 3.77/1.03 % (2668812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.03 % (2668812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.03 % (2668812)CaDiCaL version: 2.1.3
% 3.77/1.03 % (2668812)Termination reason: Instruction limit
% 3.77/1.03 % (2668812)Termination phase: Saturation
% 3.77/1.03 % (2668812)Time elapsed: 0.356 s
% 3.77/1.03 % (2668812)Peak memory usage: 13 MB
% 3.77/1.03 % (2668812)Instructions burned: 1182 (million)
% 3.77/1.03 % (2668836)ott+10_1_sil=32000:tgt=ground:random_seed=399562833:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 3.77/1.03 % (2668818)Instruction limit reached!
% 3.77/1.03 % (2668818)------------------------------
% 3.77/1.03 % (2668818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.03 % (2668818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.03 % (2668818)CaDiCaL version: 2.1.3
% 3.77/1.03 % (2668818)Termination reason: Instruction limit
% 3.77/1.03 % (2668818)Termination phase: Saturation
% 3.77/1.03 % (2668818)Time elapsed: 0.445 s
% 3.77/1.03 % (2668818)Peak memory usage: 14 MB
% 3.77/1.03 % (2668818)Instructions burned: 880 (million)
% 3.77/1.03 % (2668839)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1126445545:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 3.77/1.03 % Exception at run slice level
% 3.77/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/1.03 % (2668841)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3213604107:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 3.77/1.03 % (2668841)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.77/1.03 % (2668787) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2668781-2668787"...
% 3.77/1.03 % (2668787)...printing done.
% 3.77/1.03 % (2668787)Refutation found. Thanks to Tanya!
% 3.77/1.03 % SZS status Theorem for theBenchmark
% 3.77/1.03 % SZS output start Proof for theBenchmark
% 3.77/1.03 thf(type_def_5, type, 'type/realax/real': $tType).
% 3.77/1.03 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 3.77/1.03 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 3.77/1.03 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 3.77/1.03 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.77/1.03 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 3.77/1.03 thf(func_def_4, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 3.77/1.03 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 3.77/1.03 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.77/1.03 thf(func_def_10, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.77/1.03 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 3.77/1.03 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.77/1.03 thf(func_def_13, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.77/1.03 thf(func_def_14, type, vIMP: ($o > $o > $o)).
% 3.77/1.03 thf(func_def_15, type, sK0: 'type/realax/real').
% 3.77/1.03 thf(func_def_16, type, sK1: ('type/realax/real' > $o)).
% 3.77/1.03 thf(func_def_17, type, sK2: 'type/realax/real').
% 3.77/1.03 thf(func_def_18, type, sK3: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 3.77/1.03 thf(func_def_19, type, sK4: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 3.77/1.03 thf(func_def_21, type, sK6: 'type/realax/real').
% 3.77/1.03 thf(f1,axiom,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X1) = (X0 = X1))),
% 3.77/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_')).
% 3.77/1.03 thf(f2,axiom,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 3.77/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 3.77/1.03 thf(f3,axiom,(
% 3.77/1.03 ! [X0 : 'type/realax/real'] : ('const/realax/real_le' @ X0 @ X0)),
% 3.77/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_REFL_')).
% 3.77/1.03 thf(f4,axiom,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = ? [X2 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 3.77/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_SUP_FINITE_')).
% 3.77/1.03 thf(f5,axiom,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))))),
% 3.77/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LE_FINITE_')).
% 3.77/1.03 thf(f6,conjecture,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (((X1 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X1)) => (((('const/sets/sup' @ X1)) = X0) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) => ('const/realax/real_le' @ X2 @ X0)) & ('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))),
% 3.77/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_UNIQUE_FINITE_')).
% 3.77/1.03 thf(f7,negated_conjecture,(
% 3.77/1.03 ~ ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (((X1 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X1)) => (((('const/sets/sup' @ X1)) = X0) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) => ('const/realax/real_le' @ X2 @ X0)) & ('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))),
% 3.77/1.03 inference(negated_conjecture,[status(cth)],[f6])).
% 3.77/1.03 thf(f8,plain,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X1) = (X0 = X1))),
% 3.77/1.03 inference(rectify,[],[f1])).
% 3.77/1.03 thf(f9,plain,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0))) = ((X0 = X1)))),
% 3.77/1.03 inference(fool_elimination,[],[f8])).
% 3.77/1.03 thf(f10,plain,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 3.77/1.03 inference(rectify,[],[f2])).
% 3.77/1.03 thf(f11,plain,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ X1 @ X2)) = $true) & ((('const/realax/real_le' @ X0 @ X1)) = $true)) => ((('const/realax/real_le' @ X0 @ X2)) = $true))),
% 3.77/1.03 inference(fool_elimination,[],[f10])).
% 3.77/1.03 thf(f12,plain,(
% 3.77/1.03 ! [X0 : 'type/realax/real'] : ('const/realax/real_le' @ X0 @ X0)),
% 3.77/1.03 inference(rectify,[],[f3])).
% 3.77/1.03 thf(f13,plain,(
% 3.77/1.03 ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X0)) = $true)),
% 3.77/1.03 inference(fool_elimination,[],[f12])).
% 3.77/1.03 thf(f14,plain,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = ? [X2 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 3.77/1.03 inference(rectify,[],[f4])).
% 3.77/1.03 thf(f15,plain,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)) => ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_le' @ X1 @ Y0)))))))),
% 3.77/1.03 inference(fool_elimination,[],[f14])).
% 3.77/1.03 thf(f16,plain,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))))),
% 3.77/1.03 inference(rectify,[],[f5])).
% 3.77/1.03 thf(f17,plain,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1)))))))),
% 3.77/1.03 inference(fool_elimination,[],[f16])).
% 3.77/1.03 thf(f18,plain,(
% 3.77/1.03 ~ ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (((X1 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X1)) => (((('const/sets/sup' @ X1)) = X0) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) => ('const/realax/real_le' @ X2 @ X0)) & ('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))),
% 3.77/1.03 inference(rectify,[],[f7])).
% 3.77/1.03 thf(f19,plain,(
% 3.77/1.03 ~ ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ((('const/sets/FINITE' @ 'type/realax/real' @ X1)) = $true)) => (((('const/sets/sup' @ X1) = X0)) = ((('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X1) => ('const/realax/real_le' @ Y0 @ X0))))))))),
% 3.77/1.03 inference(fool_elimination,[],[f18])).
% 3.77/1.03 thf(f20,plain,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)))),
% 3.77/1.03 inference(ennf_transformation,[],[f11])).
% 3.77/1.03 thf(f21,plain,(
% 3.77/1.03 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true))),
% 3.77/1.03 inference(flattening,[],[f20])).
% 3.77/1.03 thf(f22,plain,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_le' @ X1 @ Y0)))))) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)))),
% 3.77/1.03 inference(ennf_transformation,[],[f15])).
% 3.77/1.03 thf(f23,plain,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_le' @ X1 @ Y0)))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true))),
% 3.77/1.03 inference(flattening,[],[f22])).
% 3.77/1.03 thf(f24,plain,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1)))))) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)))),
% 3.77/1.03 inference(ennf_transformation,[],[f17])).
% 3.77/1.03 thf(f25,plain,(
% 3.77/1.03 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1)))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true))),
% 3.77/1.03 inference(flattening,[],[f24])).
% 3.77/1.03 thf(f26,plain,(
% 3.77/1.03 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((((('const/sets/sup' @ X1) = X0)) != ((('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X1) => ('const/realax/real_le' @ Y0 @ X0))))))) & (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ((('const/sets/FINITE' @ 'type/realax/real' @ X1)) = $true)))),
% 3.77/1.03 inference(ennf_transformation,[],[f19])).
% 3.77/1.03 thf(f27,plain,(
% 3.77/1.03 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((((('const/sets/sup' @ X1) = X0)) != ((('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X1) => ('const/realax/real_le' @ Y0 @ X0))))))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1) & ((('const/sets/FINITE' @ 'type/realax/real' @ X1)) = $true))),
% 3.77/1.03 inference(flattening,[],[f26])).
% 3.77/1.03 thf(f28,plain,(
% 3.77/1.03 (((('const/sets/sup' @ sK1) = sK0)) != ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0))))))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK1) & ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK1)))),
% 3.77/1.03 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f27])).
% 3.77/1.03 thf(f29,plain,(
% 3.77/1.03 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0))) = ((X0 = X1)))) )),
% 3.77/1.03 inference(cnf_transformation,[],[f9])).
% 3.77/1.03 thf(f30,plain,(
% 3.77/1.03 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)) )),
% 3.77/1.03 inference(cnf_transformation,[],[f21])).
% 3.77/1.03 thf(f31,plain,(
% 3.77/1.03 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X0)) = $true)) )),
% 3.77/1.03 inference(cnf_transformation,[],[f13])).
% 3.77/1.03 thf(f32,plain,(
% 3.77/1.03 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_le' @ X1 @ Y0)))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)) )),
% 3.77/1.03 inference(cnf_transformation,[],[f23])).
% 3.77/1.03 thf(f33,plain,(
% 3.77/1.03 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1)))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)) )),
% 3.77/1.03 inference(cnf_transformation,[],[f25])).
% 3.77/1.03 thf(f34,plain,(
% 3.77/1.03 ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK1)))),
% 3.77/1.03 inference(cnf_transformation,[],[f28])).
% 3.77/1.03 thf(f35,plain,(
% 3.77/1.03 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 3.77/1.03 inference(cnf_transformation,[],[f28])).
% 3.77/1.03 thf(f36,plain,(
% 3.77/1.03 (((('const/sets/sup' @ sK1) = sK0)) != ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0)))))))),
% 3.77/1.03 inference(cnf_transformation,[],[f28])).
% 3.77/1.03 thf(f38,definition,(
% 3.77/1.03 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.77/1.03 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.77/1.03 thf(f39,plain,(
% 3.77/1.03 ($true = ((('const/sets/sup' @ sK1) = sK0))) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0)))))))),
% 3.77/1.03 inference(xor_proxy_clausification,[],[f36])).
% 3.77/1.03 thf(f40,plain,(
% 3.77/1.03 (((('const/sets/sup' @ sK1) = sK0)) = $false) | (((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0)))))) = $false)),
% 3.77/1.03 inference(xor_proxy_clausification,[],[f36])).
% 3.77/1.03 thf(f41,plain,(
% 3.77/1.03 (sK0 != (('const/sets/sup' @ sK1))) | (((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0)))))) = $false)),
% 3.77/1.03 inference(equality_proxy_clausification,[],[f40])).
% 3.77/1.03 thf(f42,plain,(
% 3.77/1.03 (sK0 != (('const/sets/sup' @ sK1))) | (((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0))))) = $false) | ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)) = $false)),
% 3.77/1.03 inference(and_proxy_clausification,[],[f41])).
% 3.77/1.03 thf(f43,plain,(
% 3.77/1.03 (sK0 != (('const/sets/sup' @ sK1))) | ($false = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0))) @ sK2))) | ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)) = $false)),
% 3.77/1.03 inference(sigma_proxy_clausification,[],[f42])).
% 3.77/1.03 thf(f44,plain,(
% 3.77/1.03 (sK0 != (('const/sets/sup' @ sK1))) | ($false = ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1) => ('const/realax/real_le' @ sK2 @ sK0)))) | ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)) = $false)),
% 3.77/1.03 inference(beta-eta_normalization,[],[f43])).
% 3.77/1.03 thf(f45,plain,(
% 3.77/1.03 (sK0 != (('const/sets/sup' @ sK1))) | ($false = (('const/realax/real_le' @ sK2 @ sK0))) | ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)) = $false)),
% 3.77/1.03 inference(imp_proxy_clausification,[],[f44])).
% 3.77/1.03 thf(f46,plain,(
% 3.77/1.03 (sK0 != (('const/sets/sup' @ sK1))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1))) | ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)) = $false)),
% 3.77/1.03 inference(imp_proxy_clausification,[],[f44])).
% 3.77/1.03 thf(f47,plain,(
% 3.77/1.03 (sK0 = (('const/sets/sup' @ sK1))) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0)))))))),
% 3.77/1.03 inference(equality_proxy_clausification,[],[f39])).
% 3.77/1.03 thf(f48,plain,(
% 3.77/1.03 (sK0 = (('const/sets/sup' @ sK1))) | ($true = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0))))))),
% 3.77/1.03 inference(and_proxy_clausification,[],[f47])).
% 3.77/1.03 thf(f49,plain,(
% 3.77/1.03 (sK0 = (('const/sets/sup' @ sK1))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)))),
% 3.77/1.03 inference(and_proxy_clausification,[],[f47])).
% 3.77/1.03 thf(f50,plain,(
% 3.77/1.03 ( ! [X1 : 'type/realax/real'] : ((sK0 = (('const/sets/sup' @ sK1))) | ($true = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK1) => ('const/realax/real_le' @ Y0 @ sK0))) @ X1)))) )),
% 3.77/1.03 inference(pi_proxy_clausification,[],[f48])).
% 3.77/1.03 thf(f51,plain,(
% 3.77/1.03 ( ! [X1 : 'type/realax/real'] : ((sK0 = (('const/sets/sup' @ sK1))) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) => ('const/realax/real_le' @ X1 @ sK0))))) )),
% 3.77/1.03 inference(beta-eta_normalization,[],[f50])).
% 3.77/1.03 thf(f52,plain,(
% 3.77/1.03 ( ! [X1 : 'type/realax/real'] : ((sK0 = (('const/sets/sup' @ sK1))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | ($true = (('const/realax/real_le' @ X1 @ sK0)))) )),
% 3.77/1.03 inference(imp_proxy_clausification,[],[f51])).
% 3.77/1.03 thf(f53,plain,(
% 3.77/1.03 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | (((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1))))) = $false)) )),
% 3.77/1.04 inference(iff_proxy_clausification,[],[f33])).
% 3.77/1.04 thf(f58,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ($false = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1))) @ (sK3 @ X1 @ X0))))) )),
% 3.77/1.04 inference(sigma_proxy_clausification,[],[f53])).
% 3.77/1.04 thf(f59,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ($false = ((('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0) => ('const/realax/real_le' @ (sK3 @ X1 @ X0) @ X1))))) )),
% 3.77/1.04 inference(beta-eta_normalization,[],[f58])).
% 3.77/1.04 thf(f60,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ($false = (('const/realax/real_le' @ (sK3 @ X1 @ X0) @ X1)))) )),
% 3.77/1.04 inference(imp_proxy_clausification,[],[f59])).
% 3.77/1.04 thf(f61,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0)))) )),
% 3.77/1.04 inference(imp_proxy_clausification,[],[f59])).
% 3.77/1.04 thf(f62,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | (((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_le' @ X1 @ Y0))))) = $false)) )),
% 3.77/1.04 inference(iff_proxy_clausification,[],[f32])).
% 3.77/1.04 thf(f63,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $false) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ($true = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_le' @ X1 @ Y0))))))) )),
% 3.77/1.04 inference(iff_proxy_clausification,[],[f32])).
% 3.77/1.04 thf(f64,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $false) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ($true = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_le' @ X1 @ Y0))) @ (sK4 @ X1 @ X0))))) )),
% 3.77/1.04 inference(sigma_proxy_clausification,[],[f63])).
% 3.77/1.04 thf(f65,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $false) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) & ('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0)))))) )),
% 3.77/1.04 inference(beta-eta_normalization,[],[f64])).
% 3.77/1.04 thf(f66,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $false) | ($true = (('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0))))) )),
% 3.77/1.04 inference(and_proxy_clausification,[],[f65])).
% 3.77/1.04 thf(f67,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $false) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)))) )),
% 3.77/1.04 inference(and_proxy_clausification,[],[f65])).
% 3.77/1.04 thf(f68,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ($false = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_le' @ X1 @ Y0))) @ X2)))) )),
% 3.77/1.04 inference(pi_proxy_clausification,[],[f62])).
% 3.77/1.04 thf(f69,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ($false = ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) & ('const/realax/real_le' @ X1 @ X2))))) )),
% 3.77/1.04 inference(beta-eta_normalization,[],[f68])).
% 3.77/1.04 thf(f70,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ((('const/realax/real_le' @ X1 @ X2)) = $false) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $false)) )),
% 3.77/1.04 inference(and_proxy_clausification,[],[f69])).
% 3.77/1.04 thf(f71,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0))) = $true) | (((X0 = X1)) = $false)) )),
% 3.77/1.04 inference(iff_proxy_clausification,[],[f29])).
% 3.77/1.04 thf(f72,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0))) = $false) | (((X0 = X1)) = $true)) )),
% 3.77/1.04 inference(iff_proxy_clausification,[],[f29])).
% 3.77/1.04 thf(f73,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) = $false) | (((X0 = X1)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 3.77/1.04 inference(and_proxy_clausification,[],[f72])).
% 3.77/1.04 thf(f74,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) = $false) | ((('const/realax/real_le' @ X0 @ X1)) = $false) | (X0 = X1)) )),
% 3.77/1.04 inference(equality_proxy_clausification,[],[f73])).
% 3.77/1.04 thf(f76,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1)) = $true) | (((X0 = X1)) = $false)) )),
% 3.77/1.04 inference(and_proxy_clausification,[],[f71])).
% 3.77/1.04 thf(f77,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1)) = $true) | (X0 != X1)) )),
% 3.77/1.04 inference(equality_proxy_clausification,[],[f76])).
% 3.77/1.04 thf(f80,definition,(
% 3.77/1.04 spl5_1 <=> ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)) = $false)),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 3.77/1.04 thf(f81,plain,(
% 3.77/1.04 ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)) != $false) | spl5_1),
% 3.77/1.04 inference(avatar_component_clause,[],[f80])).
% 3.77/1.04 thf(f82,plain,(
% 3.77/1.04 ((('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)) = $false) | ~spl5_1),
% 3.77/1.04 inference(avatar_component_clause,[],[f80])).
% 3.77/1.04 thf(f84,definition,(
% 3.77/1.04 spl5_2 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1)))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 3.77/1.04 thf(f86,plain,(
% 3.77/1.04 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1))) | ~spl5_2),
% 3.77/1.04 inference(avatar_component_clause,[],[f84])).
% 3.77/1.04 thf(f88,definition,(
% 3.77/1.04 spl5_3 <=> (sK0 = (('const/sets/sup' @ sK1)))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 3.77/1.04 thf(f89,plain,(
% 3.77/1.04 (sK0 = (('const/sets/sup' @ sK1))) | ~spl5_3),
% 3.77/1.04 inference(avatar_component_clause,[],[f88])).
% 3.77/1.04 thf(f90,plain,(
% 3.77/1.04 (sK0 != (('const/sets/sup' @ sK1))) | spl5_3),
% 3.77/1.04 inference(avatar_component_clause,[],[f88])).
% 3.77/1.04 thf(f91,plain,(
% 3.77/1.04 spl5_1 | spl5_2 | ~spl5_3),
% 3.77/1.04 inference(avatar_split_clause,[],[f46,f88,f84,f80])).
% 3.77/1.04 thf(f93,definition,(
% 3.77/1.04 spl5_4 <=> ($false = (('const/realax/real_le' @ sK2 @ sK0)))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 3.77/1.04 thf(f95,plain,(
% 3.77/1.04 ($false = (('const/realax/real_le' @ sK2 @ sK0))) | ~spl5_4),
% 3.77/1.04 inference(avatar_component_clause,[],[f93])).
% 3.77/1.04 thf(f96,plain,(
% 3.77/1.04 spl5_1 | spl5_4 | ~spl5_3),
% 3.77/1.04 inference(avatar_split_clause,[],[f45,f88,f93,f80])).
% 3.77/1.04 thf(f98,definition,(
% 3.77/1.04 spl5_5 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1)))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 3.77/1.04 thf(f100,plain,(
% 3.77/1.04 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1))) | ~spl5_5),
% 3.77/1.04 inference(avatar_component_clause,[],[f98])).
% 3.77/1.04 thf(f101,plain,(
% 3.77/1.04 spl5_5 | spl5_3),
% 3.77/1.04 inference(avatar_split_clause,[],[f49,f88,f98])).
% 3.77/1.04 thf(f103,definition,(
% 3.77/1.04 spl5_6 <=> ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | ($true = (('const/realax/real_le' @ X1 @ sK0))))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 3.77/1.04 thf(f104,plain,(
% 3.77/1.04 ( ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | ($true = (('const/realax/real_le' @ X1 @ sK0)))) ) | ~spl5_6),
% 3.77/1.04 inference(avatar_component_clause,[],[f103])).
% 3.77/1.04 thf(f105,plain,(
% 3.77/1.04 spl5_6 | spl5_3),
% 3.77/1.04 inference(avatar_split_clause,[],[f52,f88,f103])).
% 3.77/1.04 thf(f135,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ X2 @ X1)) = $true) | ((('const/realax/real_le' @ X2 @ X0)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 3.77/1.04 inference(constrained_superposition,[],[f30,f38])).
% 3.77/1.04 thf(f136,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X0)) != $true) | ((('const/realax/real_le' @ X2 @ X1)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f135])).
% 3.77/1.04 thf(f150,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) = $false) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 3.77/1.04 inference(constrained_superposition,[],[f136,f38])).
% 3.77/1.04 thf(f151,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) = $false) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f150])).
% 3.77/1.04 thf(f158,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)))) | ((('const/realax/real_le' @ X0 @ X1)) = $false) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1)))) )),
% 3.77/1.04 inference(constrained_superposition,[],[f70,f34])).
% 3.77/1.04 thf(f159,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ((('const/realax/real_le' @ X1 @ X2)) = $false) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $false) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $false)) )),
% 3.77/1.04 inference(constrained_superposition,[],[f70,f38])).
% 3.77/1.04 thf(f160,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $false) | ((('const/realax/real_le' @ X1 @ X2)) = $false) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $false)) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f159])).
% 3.77/1.04 thf(f161,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)))) | ((('const/realax/real_le' @ X0 @ X1)) = $false) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1)))) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f158])).
% 3.77/1.04 thf(f162,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)))) | ((('const/realax/real_le' @ X0 @ X1)) = $false) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1)))) )),
% 3.77/1.04 inference(forward_subsumption_resolution,[],[f161,f35])).
% 3.77/1.04 thf(f249,plain,(
% 3.77/1.04 ($true = $false) | (~spl5_1 | ~spl5_5)),
% 3.77/1.04 inference(forward_demodulation,[],[f100,f82])).
% 3.77/1.04 thf(f250,plain,(
% 3.77/1.04 $false | (~spl5_1 | ~spl5_5)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f249])).
% 3.77/1.04 thf(f251,plain,(
% 3.77/1.04 ~spl5_1 | ~spl5_5),
% 3.77/1.04 inference(avatar_contradiction_clause,[],[f250])).
% 3.77/1.04 thf(f254,plain,(
% 3.77/1.04 ($true = $false) | ($true = (('const/realax/real_le' @ sK2 @ sK0))) | (~spl5_2 | ~spl5_6)),
% 3.77/1.04 inference(constrained_superposition,[],[f104,f86])).
% 3.77/1.04 thf(f265,plain,(
% 3.77/1.04 ($true = (('const/realax/real_le' @ sK2 @ sK0))) | (~spl5_2 | ~spl5_6)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f254])).
% 3.77/1.04 thf(f269,plain,(
% 3.77/1.04 ($true = $false) | (~spl5_2 | ~spl5_4 | ~spl5_6)),
% 3.77/1.04 inference(forward_demodulation,[],[f265,f95])).
% 3.77/1.04 thf(f270,plain,(
% 3.77/1.04 $false | (~spl5_2 | ~spl5_4 | ~spl5_6)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f269])).
% 3.77/1.04 thf(f271,plain,(
% 3.77/1.04 ~spl5_2 | ~spl5_4 | ~spl5_6),
% 3.77/1.04 inference(avatar_contradiction_clause,[],[f270])).
% 3.77/1.04 thf(f293,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ sK0))) | ((('const/realax/real_le' @ X0 @ X1)) = $false) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1)))) ) | ~spl5_3),
% 3.77/1.04 inference(forward_demodulation,[],[f162,f89])).
% 3.77/1.04 thf(f303,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)))) ) | ~spl5_3),
% 3.77/1.04 inference(constrained_superposition,[],[f31,f293])).
% 3.77/1.04 thf(f308,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)))) ) | ~spl5_3),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f303])).
% 3.77/1.04 thf(f318,plain,(
% 3.77/1.04 spl5_6 | ~spl5_3),
% 3.77/1.04 inference(avatar_split_clause,[],[f308,f88,f103])).
% 3.77/1.04 thf(f330,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | (X0 != X1)) ) | ~spl5_3),
% 3.77/1.04 inference(constrained_superposition,[],[f293,f77])).
% 3.77/1.04 thf(f339,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | (X0 != X1)) ) | ~spl5_3),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f330])).
% 3.77/1.04 thf(f438,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($false = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ X0)))) )),
% 3.77/1.04 inference(constrained_superposition,[],[f60,f34])).
% 3.77/1.04 thf(f441,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($false = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ X0)))) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f438])).
% 3.77/1.04 thf(f442,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) )),
% 3.77/1.04 inference(forward_subsumption_resolution,[],[f441,f35])).
% 3.77/1.04 thf(f444,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($false = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))))) )),
% 3.77/1.04 inference(constrained_superposition,[],[f66,f34])).
% 3.77/1.04 thf(f447,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($false = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))))) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f444])).
% 3.77/1.04 thf(f448,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1)))) | ($false = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))))) )),
% 3.77/1.04 inference(forward_subsumption_resolution,[],[f447,f35])).
% 3.77/1.04 thf(f449,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1)))) | ($false = (('const/realax/real_le' @ X0 @ sK0)))) ) | ~spl5_3),
% 3.77/1.04 inference(forward_demodulation,[],[f448,f89])).
% 3.77/1.04 thf(f523,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true = $false) | ($false = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))) | ((('const/sets/sup' @ X1)) = X0) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) = $false) | ((('const/realax/real_le' @ X0 @ X2)) = $false) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ((('const/sets/FINITE' @ 'type/realax/real' @ X1)) = $false)) )),
% 3.77/1.04 inference(constrained_superposition,[],[f74,f160])).
% 3.77/1.04 thf(f545,plain,(
% 3.77/1.04 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($false = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) = $false) | ((('const/realax/real_le' @ X0 @ X2)) = $false) | ((('const/sets/sup' @ X1)) = X0) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ((('const/sets/FINITE' @ 'type/realax/real' @ X1)) = $false)) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f523])).
% 3.77/1.04 thf(f563,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0))) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $false)) )),
% 3.77/1.04 inference(constrained_superposition,[],[f61,f38])).
% 3.77/1.04 thf(f564,plain,(
% 3.77/1.04 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $false)) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f563])).
% 3.77/1.04 thf(f568,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($false = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)))) )),
% 3.77/1.04 inference(constrained_superposition,[],[f67,f34])).
% 3.77/1.04 thf(f571,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($false = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)))) )),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f568])).
% 3.77/1.04 thf(f572,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1))) | ($false = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))))) )),
% 3.77/1.04 inference(forward_subsumption_resolution,[],[f571,f35])).
% 3.77/1.04 thf(f573,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1))) | ($false = (('const/realax/real_le' @ X0 @ sK0)))) ) | ~spl5_3),
% 3.77/1.04 inference(forward_demodulation,[],[f572,f89])).
% 3.77/1.04 thf(f583,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($false = (('const/realax/real_le' @ sK0 @ X0))) | (sK0 = X0) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | (X0 != X1)) ) | ~spl5_3),
% 3.77/1.04 inference(constrained_superposition,[],[f74,f339])).
% 3.77/1.04 thf(f595,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ X0))) | (sK0 = X0) | (X0 != X1)) ) | ~spl5_3),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f583])).
% 3.77/1.04 thf(f967,definition,(
% 3.77/1.04 spl5_14 <=> ! [X1 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ sK0 @ X1))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_14])],[avatar_definition])).
% 3.77/1.04 thf(f968,plain,(
% 3.77/1.04 ( ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ X1)))) ) | ~spl5_14),
% 3.77/1.04 inference(avatar_component_clause,[],[f967])).
% 3.77/1.04 thf(f1374,definition,(
% 3.77/1.04 spl5_18 <=> ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/realax/real_le' @ sK0 @ X0))))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition])).
% 3.77/1.04 thf(f1375,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | ~spl5_18),
% 3.77/1.04 inference(avatar_component_clause,[],[f1374])).
% 3.77/1.04 thf(f1389,plain,(
% 3.77/1.04 ($true = $false) | ($true = $false) | ~spl5_18),
% 3.77/1.04 inference(constrained_superposition,[],[f1375,f31])).
% 3.77/1.04 thf(f1446,plain,(
% 3.77/1.04 ($true = $false) | ~spl5_18),
% 3.77/1.04 inference(duplicate_literal_removal,[],[f1389])).
% 3.77/1.04 thf(f1447,plain,(
% 3.77/1.04 $false | ~spl5_18),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f1446])).
% 3.77/1.04 thf(f1448,plain,(
% 3.77/1.04 ~spl5_18),
% 3.77/1.04 inference(avatar_contradiction_clause,[],[f1447])).
% 3.77/1.04 thf(f3588,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK1)) = $false)) ) | ~spl5_6),
% 3.77/1.04 inference(constrained_superposition,[],[f104,f564])).
% 3.77/1.04 thf(f3628,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK1)) = $false)) ) | ~spl5_6),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f3588])).
% 3.77/1.04 thf(f3664,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK1)) = $false)) ) | ~spl5_6),
% 3.77/1.04 inference(forward_subsumption_resolution,[],[f3628,f35])).
% 3.77/1.04 thf(f6856,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | (sK0 = ((sK4 @ sK0 @ sK1))) | (((sK4 @ sK0 @ sK1)) != X0) | ($false = (('const/realax/real_le' @ sK0 @ sK0)))) ) | ~spl5_3),
% 3.77/1.04 inference(constrained_superposition,[],[f595,f449])).
% 3.77/1.04 thf(f6905,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | (sK0 = ((sK4 @ sK0 @ sK1))) | (((sK4 @ sK0 @ sK1)) != X0) | ($false = (('const/realax/real_le' @ sK0 @ sK0)))) ) | ~spl5_3),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f6856])).
% 3.77/1.04 thf(f6928,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | (sK0 = ((sK4 @ sK0 @ sK1))) | (((sK4 @ sK0 @ sK1)) != X0)) ) | ~spl5_3),
% 3.77/1.04 inference(forward_demodulation,[],[f6905,f31])).
% 3.77/1.04 thf(f6929,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | (sK0 = ((sK4 @ sK0 @ sK1))) | (((sK4 @ sK0 @ sK1)) != X0)) ) | ~spl5_3),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f6928])).
% 3.77/1.04 thf(f6933,definition,(
% 3.77/1.04 spl5_23 <=> (sK0 = ((sK4 @ sK0 @ sK1)))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_23])],[avatar_definition])).
% 3.77/1.04 thf(f6935,plain,(
% 3.77/1.04 (sK0 = ((sK4 @ sK0 @ sK1))) | ~spl5_23),
% 3.77/1.04 inference(avatar_component_clause,[],[f6933])).
% 3.77/1.04 thf(f6937,definition,(
% 3.77/1.04 spl5_24 <=> ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | (((sK4 @ sK0 @ sK1)) != X0))),
% 3.77/1.04 introduced(definition,[new_symbols(definition,[spl5_24])],[avatar_definition])).
% 3.77/1.04 thf(f6938,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : ((((sK4 @ sK0 @ sK1)) != X0) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)))) ) | ~spl5_24),
% 3.77/1.04 inference(avatar_component_clause,[],[f6937])).
% 3.77/1.04 thf(f6942,plain,(
% 3.77/1.04 spl5_23 | spl5_24 | ~spl5_3),
% 3.77/1.04 inference(avatar_split_clause,[],[f6929,f88,f6937,f6933])).
% 3.77/1.04 thf(f6954,plain,(
% 3.77/1.04 ($false = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ sK0 @ sK1) @ sK1))) | ~spl5_24),
% 3.77/1.04 inference(equality_resolution,[],[f6938])).
% 3.77/1.04 thf(f6958,plain,(
% 3.77/1.04 ($true = $false) | ($false = (('const/realax/real_le' @ sK0 @ sK0))) | (~spl5_3 | ~spl5_24)),
% 3.77/1.04 inference(constrained_superposition,[],[f573,f6954])).
% 3.77/1.04 thf(f6961,plain,(
% 3.77/1.04 ($false = (('const/realax/real_le' @ sK0 @ sK0))) | (~spl5_3 | ~spl5_24)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f6958])).
% 3.77/1.04 thf(f6984,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | (~spl5_3 | ~spl5_24)),
% 3.77/1.04 inference(constrained_superposition,[],[f151,f6961])).
% 3.77/1.04 thf(f6997,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | (~spl5_3 | ~spl5_24)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f6984])).
% 3.77/1.04 thf(f7011,plain,(
% 3.77/1.04 spl5_18 | ~spl5_3 | ~spl5_24),
% 3.77/1.04 inference(avatar_split_clause,[],[f6997,f6937,f88,f1374])).
% 3.77/1.04 thf(f7013,plain,(
% 3.77/1.04 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK0 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ sK0))) | (~spl5_3 | ~spl5_23)),
% 3.77/1.04 inference(constrained_superposition,[],[f573,f6935])).
% 3.77/1.04 thf(f7018,plain,(
% 3.77/1.04 ($true = $false) | ($false = (('const/realax/real_le' @ sK0 @ sK0))) | (~spl5_1 | ~spl5_3 | ~spl5_23)),
% 3.77/1.04 inference(forward_demodulation,[],[f7013,f82])).
% 3.77/1.04 thf(f7019,plain,(
% 3.77/1.04 ($false = (('const/realax/real_le' @ sK0 @ sK0))) | (~spl5_1 | ~spl5_3 | ~spl5_23)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f7018])).
% 3.77/1.04 thf(f7036,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | (~spl5_1 | ~spl5_3 | ~spl5_23)),
% 3.77/1.04 inference(constrained_superposition,[],[f151,f7019])).
% 3.77/1.04 thf(f7049,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | (~spl5_1 | ~spl5_3 | ~spl5_23)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f7036])).
% 3.77/1.04 thf(f7063,plain,(
% 3.77/1.04 spl5_18 | ~spl5_1 | ~spl5_3 | ~spl5_23),
% 3.77/1.04 inference(avatar_split_clause,[],[f7049,f6933,f88,f80,f1374])).
% 3.77/1.04 thf(f7079,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | ~spl5_6),
% 3.77/1.04 inference(forward_demodulation,[],[f3664,f34])).
% 3.77/1.04 thf(f7080,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | ~spl5_6),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f7079])).
% 3.77/1.04 thf(f10445,plain,(
% 3.77/1.04 ($false != $false) | ($false = (('const/realax/real_le' @ sK0 @ sK0))) | (spl5_1 | ~spl5_14)),
% 3.77/1.04 inference(constrained_superposition,[],[f81,f968])).
% 3.77/1.04 thf(f10450,plain,(
% 3.77/1.04 ($false = (('const/realax/real_le' @ sK0 @ sK0))) | (spl5_1 | ~spl5_14)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f10445])).
% 3.77/1.04 thf(f12288,plain,(
% 3.77/1.04 ($true = $false) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ~spl5_6),
% 3.77/1.04 inference(constrained_superposition,[],[f442,f7080])).
% 3.77/1.04 thf(f12289,plain,(
% 3.77/1.04 ($true = $false) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ~spl5_6),
% 3.77/1.04 inference(duplicate_literal_removal,[],[f12288])).
% 3.77/1.04 thf(f12290,plain,(
% 3.77/1.04 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ~spl5_6),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f12289])).
% 3.77/1.04 thf(f12409,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ X0))) | (sK0 = (('const/sets/sup' @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK1)) = $false)) ) | ~spl5_6),
% 3.77/1.04 inference(constrained_superposition,[],[f545,f12290])).
% 3.77/1.04 thf(f12422,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ X0))) | (sK0 = (('const/sets/sup' @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK1)) = $false)) ) | ~spl5_6),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f12409])).
% 3.77/1.04 thf(f12480,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK1)) = $false)) ) | (spl5_3 | ~spl5_6)),
% 3.77/1.04 inference(forward_subsumption_resolution,[],[f12422,f90])).
% 3.77/1.04 thf(f12492,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ X0))) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK1)) = $false)) ) | (spl5_3 | ~spl5_6)),
% 3.77/1.04 inference(forward_subsumption_resolution,[],[f12480,f35])).
% 3.77/1.04 thf(f12503,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | (spl5_3 | ~spl5_6)),
% 3.77/1.04 inference(forward_demodulation,[],[f12492,f34])).
% 3.77/1.04 thf(f12504,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | (spl5_3 | ~spl5_6)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f12503])).
% 3.77/1.04 thf(f12507,plain,(
% 3.77/1.04 spl5_14 | spl5_3 | ~spl5_6),
% 3.77/1.04 inference(avatar_split_clause,[],[f12504,f103,f88,f967])).
% 3.77/1.04 thf(f12828,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | (spl5_1 | ~spl5_14)),
% 3.77/1.04 inference(constrained_superposition,[],[f151,f10450])).
% 3.77/1.04 thf(f12841,plain,(
% 3.77/1.04 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ sK0))) | ($false = (('const/realax/real_le' @ sK0 @ X0)))) ) | (spl5_1 | ~spl5_14)),
% 3.77/1.04 inference(trivial_inequality_removal,[],[f12828])).
% 3.77/1.04 thf(f12855,plain,(
% 3.77/1.04 spl5_18 | spl5_1 | ~spl5_14),
% 3.77/1.04 inference(avatar_split_clause,[],[f12841,f967,f80,f1374])).
% 3.77/1.04 cnf(s1, plain, spl5_1 | spl5_2 | ~spl5_3, inference(sat_conversion,[],[f91])).
% 3.77/1.04 cnf(s2, plain, spl5_1 | ~spl5_3 | spl5_4, inference(sat_conversion,[],[f96])).
% 3.77/1.04 cnf(s3, plain, spl5_3 | spl5_5, inference(sat_conversion,[],[f101])).
% 3.77/1.04 cnf(s4, plain, spl5_3 | spl5_6, inference(sat_conversion,[],[f105])).
% 3.77/1.04 cnf(s12, plain, ~spl5_1 | ~spl5_5, inference(sat_conversion,[],[f251])).
% 3.77/1.04 cnf(s14, plain, ~spl5_2 | ~spl5_4 | ~spl5_6, inference(sat_conversion,[],[f271])).
% 3.77/1.04 cnf(s20, plain, ~spl5_3 | spl5_6, inference(sat_conversion,[],[f318])).
% 3.77/1.04 cnf(s36, plain, ~spl5_18, inference(sat_conversion,[],[f1448])).
% 3.77/1.04 cnf(s63, plain, ~spl5_3 | spl5_23 | spl5_24, inference(sat_conversion,[],[f6942])).
% 3.77/1.04 cnf(s68, plain, ~spl5_3 | spl5_18 | ~spl5_24, inference(sat_conversion,[],[f7011])).
% 3.77/1.04 cnf(s74, plain, ~spl5_1 | ~spl5_3 | spl5_18 | ~spl5_23, inference(sat_conversion,[],[f7063])).
% 3.77/1.04 cnf(s209, plain, spl5_3 | ~spl5_6 | spl5_14, inference(sat_conversion,[],[f12507])).
% 3.77/1.04 cnf(s225, plain, spl5_1 | ~spl5_14 | spl5_18, inference(sat_conversion,[],[f12855])).
% 3.77/1.04 cnf(s229, plain, spl5_3 | spl5_14, inference(rat,[],[s209,s4])).
% 3.77/1.04 cnf(s230, plain, spl5_1, inference(rat,[],[s14,s1,s2,s20,s229,s225,s36])).
% 3.77/1.04 cnf(s231, plain, ~spl5_5, inference(rat,[],[s12,s230])).
% 3.77/1.04 cnf(s232, plain, spl5_3, inference(rat,[],[s3,s231])).
% 3.77/1.04 cnf(s233, plain, ~spl5_23, inference(rat,[],[s74,s230,s36,s232])).
% 3.77/1.04 cnf(s234, plain, ~spl5_24, inference(rat,[],[s68,s36,s232])).
% 3.77/1.04 cnf(s235, plain, $false, inference(rat,[],[s63,s234,s233,s232])).
% 3.77/1.04 thf(f12856,plain,(
% 3.77/1.04 $false),
% 3.77/1.04 inference(avatar_sat_refutation,[],[s235])).
% 3.77/1.04 % SZS output end Proof for theBenchmark
% 3.77/1.04 % (2668787)------------------------------
% 3.77/1.04 % (2668787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/1.04 % (2668787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.04 % (2668787)CaDiCaL version: 2.1.3
% 3.77/1.04 % (2668787)Termination reason: Refutation
% 3.77/1.04 % (2668787)Time elapsed: 0.760 s
% 3.77/1.04 % (2668787)Peak memory usage: 15 MB
% 3.77/1.04 % (2668787)Instructions burned: 1689 (million)
% 3.77/1.04 % (2668781)Success in time 0.799 s
% 3.77/1.04 % Vampire exiting
%------------------------------------------------------------------------------