%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM766^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:19:29 AM UTC 2026
% Result : Theorem 3.53s 0.85s
% Output : Refutation 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM766^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:56:11 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 3.53/0.85 % (27981)Will run a generic schedule for satisfiability detection.
% 3.53/0.85 % (28006)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=112061150:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.53/0.85 % (28002)% WARNING: option uhcvi not known.
% 3.53/0.85 % (28000)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1708568758_2999 on theBenchmark for (2999ds/0Mi)
% 3.53/0.85 % (28004)dis+10_1_sil=32000:sp=arity:random_seed=222958361:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.53/0.85 % (28003)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3297369085:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.53/0.85 % (28007)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2261849999:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.53/0.85 % (28005)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=111831396:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28002)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3682711612:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.53/0.85 % (28005)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.53/0.85 % (28002)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.53/0.85 % (28002)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.53/0.85 % (28020)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3986785479:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28006)Instruction limit reached!
% 3.53/0.85 % (28006)------------------------------
% 3.53/0.85 % (28006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28006)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28006)Termination reason: Instruction limit
% 3.53/0.85 % (28006)Termination phase: Saturation
% 3.53/0.85 % (28006)Time elapsed: 0.037 s
% 3.53/0.85 % (28006)Peak memory usage: 12 MB
% 3.53/0.85 % (28006)Instructions burned: 132 (million)
% 3.53/0.85 % (28024)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=406877402:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.53/0.85 % (28025)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=1234023986:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.53/0.85 % (28025)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.53/0.85 % (28025)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.53/0.85 % (28004)Instruction limit reached!
% 3.53/0.85 % (28004)------------------------------
% 3.53/0.85 % (28004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28004)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28004)Termination reason: Instruction limit
% 3.53/0.85 % (28004)Termination phase: Saturation
% 3.53/0.85 % (28004)Time elapsed: 0.054 s
% 3.53/0.85 % (28004)Peak memory usage: 12 MB
% 3.53/0.85 % (28004)Instructions burned: 109 (million)
% 3.53/0.85 % (28005)Instruction limit reached!
% 3.53/0.85 % (28005)------------------------------
% 3.53/0.85 % (28005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28005)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28005)Termination reason: Instruction limit
% 3.53/0.85 % (28005)Termination phase: Saturation
% 3.53/0.85 % (28005)Time elapsed: 0.060 s
% 3.53/0.85 % (28005)Peak memory usage: 12 MB
% 3.53/0.85 % (28005)Instructions burned: 117 (million)
% 3.53/0.85 % (28035)ott-21_1_sil=16000:fs=off:random_seed=144987855:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.53/0.85 % (28007)Instruction limit reached!
% 3.53/0.85 % (28007)------------------------------
% 3.53/0.85 % (28007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28007)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28007)Termination reason: Instruction limit
% 3.53/0.85 % (28007)Termination phase: Saturation
% 3.53/0.85 % (28007)Time elapsed: 0.080 s
% 3.53/0.85 % (28007)Peak memory usage: 12 MB
% 3.53/0.85 % (28007)Instructions burned: 159 (million)
% 3.53/0.85 % (28038)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3110565380:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 3.53/0.85 % (28045)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1639342991:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28051)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3734567063:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.53/0.85 % (28024)Instruction limit reached!
% 3.53/0.85 % (28024)------------------------------
% 3.53/0.85 % (28024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28024)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28024)Termination reason: Instruction limit
% 3.53/0.85 % (28024)Termination phase: Saturation
% 3.53/0.85 % (28024)Time elapsed: 0.089 s
% 3.53/0.85 % (28024)Peak memory usage: 12 MB
% 3.53/0.85 % (28024)Instructions burned: 132 (million)
% 3.53/0.85 % (28053)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2206299710:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28035)Instruction limit reached!
% 3.53/0.85 % (28035)------------------------------
% 3.53/0.85 % (28035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28035)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28035)Termination reason: Instruction limit
% 3.53/0.85 % (28035)Termination phase: Saturation
% 3.53/0.85 % (28035)Time elapsed: 0.087 s
% 3.53/0.85 % (28035)Peak memory usage: 12 MB
% 3.53/0.85 % (28035)Instructions burned: 180 (million)
% 3.53/0.85 % (28066)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=3320604549: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)
% 3.53/0.85 % (28066)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.53/0.85 % (28069)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1899110928:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 3.53/0.85 % (28069)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.53/0.85 % (28025)Instruction limit reached!
% 3.53/0.85 % (28025)------------------------------
% 3.53/0.85 % (28025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28025)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28025)Termination reason: Instruction limit
% 3.53/0.85 % (28025)Termination phase: Saturation
% 3.53/0.85 % (28025)Time elapsed: 0.171 s
% 3.53/0.85 % (28025)Peak memory usage: 14 MB
% 3.53/0.85 % (28025)Instructions burned: 686 (million)
% 3.53/0.85 % (28081)fmb+10_1_sil=64000:random_seed=1357461461:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.53/0.85 % (28081)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28089)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=6044168:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28098)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3761116929:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28104)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3791738252:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.53/0.85 % (28104)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.53/0.85 % (28038)Instruction limit reached!
% 3.53/0.85 % (28038)------------------------------
% 3.53/0.85 % (28038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28038)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28038)Termination reason: Instruction limit
% 3.53/0.85 % (28038)Termination phase: Saturation
% 3.53/0.85 % (28038)Time elapsed: 0.283 s
% 3.53/0.85 % (28038)Peak memory usage: 13 MB
% 3.53/0.85 % (28038)Instructions burned: 477 (million)
% 3.53/0.85 % (28126)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1527284087:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 3.53/0.85 % (28126)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.53/0.85 % (28126)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.53/0.85 % (28066)Instruction limit reached!
% 3.53/0.85 % (28066)------------------------------
% 3.53/0.85 % (28066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28066)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28066)Termination reason: Instruction limit
% 3.53/0.85 % (28066)Termination phase: Saturation
% 3.53/0.85 % (28066)Time elapsed: 0.254 s
% 3.53/0.85 % (28066)Peak memory usage: 15 MB
% 3.53/0.85 % (28066)Instructions burned: 693 (million)
% 3.53/0.85 % (28132)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=557626872:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28136)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3559468448:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 3.53/0.85 % Exception at run slice level
% 3.53/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.53/0.85 % (28139)ott-2_1_sil=16000:newcnf=on:random_seed=2813636544:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 3.53/0.85 % (28139)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.53/0.85 % (28002) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-27981-28002"...
% 3.53/0.85 % (28002)...printing done.
% 3.53/0.85 % (28002)Refutation found. Thanks to Tanya!
% 3.53/0.85 % SZS status Theorem for theBenchmark
% 3.53/0.85 % SZS output start Proof for theBenchmark
% 3.53/0.85 thf(type_def_5, type, frac: $tType).
% 3.53/0.85 thf(type_def_6, type, nat: $tType).
% 3.53/0.85 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 3.53/0.85 thf(func_def_0, type, x: frac).
% 3.53/0.85 thf(func_def_1, type, y: frac).
% 3.53/0.85 thf(func_def_2, type, ts: (nat > nat > nat)).
% 3.53/0.85 thf(func_def_3, type, num: (frac > nat)).
% 3.53/0.85 thf(func_def_4, type, den: (frac > nat)).
% 3.53/0.85 thf(func_def_5, type, pl: (nat > nat > nat)).
% 3.53/0.85 thf(func_def_7, type, eq: (frac > frac > $o)).
% 3.53/0.85 thf(func_def_8, type, pf: (frac > frac > frac)).
% 3.53/0.85 thf(func_def_9, type, fr: (nat > nat > frac)).
% 3.53/0.85 thf(func_def_10, type, ind: ((nat > $o) > nat)).
% 3.53/0.85 thf(func_def_11, type, amone: ((nat > $o) > $o)).
% 3.53/0.85 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 3.53/0.85 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.53/0.85 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.53/0.85 thf(func_def_17, type, sK0: nat).
% 3.53/0.85 thf(func_def_18, type, vNOT: ($o > $o)).
% 3.53/0.85 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 3.53/0.85 thf(f1,axiom,(
% 3.53/0.85 ~ ! [X0 : nat] : (((ts @ (num @ x) @ (den @ y))) != ((pl @ (ts @ (num @ y) @ (den @ x)) @ X0)))),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m)).
% 3.53/0.85 thf(f3,axiom,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => ((eq @ X1 @ X2) => (eq @ X0 @ X2)))),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39)).
% 3.53/0.85 thf(f4,axiom,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56)).
% 3.53/0.85 thf(f5,axiom,(
% 3.53/0.85 ! [X0 : frac,X1 : nat] : (eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)))),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz40)).
% 3.53/0.85 thf(f6,axiom,(
% 3.53/0.85 ! [X0 : frac] : (eq @ X0 @ X0)),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37)).
% 3.53/0.85 thf(f7,axiom,(
% 3.53/0.85 ! [X0 : nat,X1 : nat] : (((ts @ X0 @ X1)) = ((ts @ X1 @ X0)))),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29)).
% 3.53/0.85 thf(f8,axiom,(
% 3.53/0.85 ! [X0 : nat,X1 : nat,X2 : nat] : (eq @ (pf @ (fr @ X0 @ X2) @ (fr @ X1 @ X2)) @ (fr @ (pl @ X0 @ X1) @ X2))),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz57)).
% 3.53/0.85 thf(f10,axiom,(
% 3.53/0.85 ! [X0 : frac,X1 : nat] : (eq @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X0)),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz40a)).
% 3.53/0.85 thf(f11,conjecture,(
% 3.53/0.85 ~ ! [X0 : frac] : ~(eq @ (pf @ y @ X0) @ x)),
% 3.53/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz67a)).
% 3.53/0.85 thf(f12,negated_conjecture,(
% 3.53/0.85 ~ ~ ! [X0 : frac] : ~(eq @ (pf @ y @ X0) @ x)),
% 3.53/0.85 inference(negated_conjecture,[status(cth)],[f11])).
% 3.53/0.85 thf(f15,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => ((eq @ X1 @ X2) => (eq @ X0 @ X2)))),
% 3.53/0.85 inference(rectify,[],[f3])).
% 3.53/0.85 thf(f16,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac] : ((((eq @ X0 @ X1)) = $true) => ((((eq @ X1 @ X2)) = $true) => (((eq @ X0 @ X2)) = $true)))),
% 3.53/0.85 inference(fool_elimination,[],[f15])).
% 3.53/0.85 thf(f17,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 3.53/0.85 inference(rectify,[],[f4])).
% 3.53/0.85 thf(f18,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ X0 @ X1)) = $true) => ((((eq @ X2 @ X3)) = $true) => (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)))),
% 3.53/0.85 inference(fool_elimination,[],[f17])).
% 3.53/0.85 thf(f19,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : nat] : (eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)))),
% 3.53/0.85 inference(rectify,[],[f5])).
% 3.53/0.85 thf(f20,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : nat] : (((eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)))) = $true)),
% 3.53/0.85 inference(fool_elimination,[],[f19])).
% 3.53/0.85 thf(f21,plain,(
% 3.53/0.85 ! [X0 : frac] : (eq @ X0 @ X0)),
% 3.53/0.85 inference(rectify,[],[f6])).
% 3.53/0.85 thf(f22,plain,(
% 3.53/0.85 ! [X0 : frac] : (((eq @ X0 @ X0)) = $true)),
% 3.53/0.85 inference(fool_elimination,[],[f21])).
% 3.53/0.85 thf(f23,plain,(
% 3.53/0.85 ! [X0 : nat,X1 : nat,X2 : nat] : (eq @ (pf @ (fr @ X0 @ X2) @ (fr @ X1 @ X2)) @ (fr @ (pl @ X0 @ X1) @ X2))),
% 3.53/0.85 inference(rectify,[],[f8])).
% 3.53/0.85 thf(f24,plain,(
% 3.53/0.85 ! [X0 : nat,X1 : nat,X2 : nat] : (((eq @ (pf @ (fr @ X0 @ X2) @ (fr @ X1 @ X2)) @ (fr @ (pl @ X0 @ X1) @ X2))) = $true)),
% 3.53/0.85 inference(fool_elimination,[],[f23])).
% 3.53/0.85 thf(f27,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : nat] : (eq @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X0)),
% 3.53/0.85 inference(rectify,[],[f10])).
% 3.53/0.85 thf(f28,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : nat] : (((eq @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X0)) = $true)),
% 3.53/0.85 inference(fool_elimination,[],[f27])).
% 3.53/0.85 thf(f29,plain,(
% 3.53/0.85 ~ ~ ! [X0 : frac] : ~(eq @ (pf @ y @ X0) @ x)),
% 3.53/0.85 inference(rectify,[],[f12])).
% 3.53/0.85 thf(f30,plain,(
% 3.53/0.85 ~ ~ ! [X0 : frac] : ~ (((eq @ (pf @ y @ X0) @ x)) = $true)),
% 3.53/0.85 inference(fool_elimination,[],[f29])).
% 3.53/0.85 thf(f32,plain,(
% 3.53/0.85 ! [X0 : frac] : (((eq @ (pf @ y @ X0) @ x)) != $true)),
% 3.53/0.85 inference(flattening,[],[f30])).
% 3.53/0.85 thf(f33,plain,(
% 3.53/0.85 ? [X0 : nat] : (((ts @ (num @ x) @ (den @ y))) = ((pl @ (ts @ (num @ y) @ (den @ x)) @ X0)))),
% 3.53/0.85 inference(ennf_transformation,[],[f1])).
% 3.53/0.85 thf(f34,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac] : (((((eq @ X0 @ X2)) = $true) | (((eq @ X1 @ X2)) != $true)) | (((eq @ X0 @ X1)) != $true))),
% 3.53/0.85 inference(ennf_transformation,[],[f16])).
% 3.53/0.85 thf(f35,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac] : ((((eq @ X0 @ X2)) = $true) | (((eq @ X1 @ X2)) != $true) | (((eq @ X0 @ X1)) != $true))),
% 3.53/0.85 inference(flattening,[],[f34])).
% 3.53/0.85 thf(f36,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X2 @ X3)) != $true)) | (((eq @ X0 @ X1)) != $true))),
% 3.53/0.85 inference(ennf_transformation,[],[f18])).
% 3.53/0.85 thf(f37,plain,(
% 3.53/0.85 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X2 @ X3)) != $true) | (((eq @ X0 @ X1)) != $true))),
% 3.53/0.85 inference(flattening,[],[f36])).
% 3.53/0.85 thf(f40,plain,(
% 3.53/0.85 (((ts @ (num @ x) @ (den @ y))) = ((pl @ (ts @ (num @ y) @ (den @ x)) @ sK0)))),
% 3.53/0.85 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f33])).
% 3.53/0.85 thf(f41,plain,(
% 3.53/0.85 (((ts @ (num @ x) @ (den @ y))) = ((pl @ (ts @ (num @ y) @ (den @ x)) @ sK0)))),
% 3.53/0.85 inference(cnf_transformation,[],[f40])).
% 3.53/0.85 thf(f43,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((eq @ X1 @ X2)) != $true) | (((eq @ X0 @ X2)) = $true) | (((eq @ X0 @ X1)) != $true)) )),
% 3.53/0.85 inference(cnf_transformation,[],[f35])).
% 3.53/0.85 thf(f44,plain,(
% 3.53/0.85 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((eq @ X2 @ X3)) != $true) | (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X0 @ X1)) != $true)) )),
% 3.53/0.85 inference(cnf_transformation,[],[f37])).
% 3.53/0.85 thf(f45,plain,(
% 3.53/0.85 ( ! [X0 : frac,X1 : nat] : ((((eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)))) = $true)) )),
% 3.53/0.85 inference(cnf_transformation,[],[f20])).
% 3.53/0.85 thf(f46,plain,(
% 3.53/0.85 ( ! [X0 : frac] : ((((eq @ X0 @ X0)) = $true)) )),
% 3.53/0.85 inference(cnf_transformation,[],[f22])).
% 3.53/0.85 thf(f47,plain,(
% 3.53/0.85 ( ! [X0 : nat,X1 : nat] : ((((ts @ X0 @ X1)) = ((ts @ X1 @ X0)))) )),
% 3.53/0.85 inference(cnf_transformation,[],[f7])).
% 3.53/0.85 thf(f48,plain,(
% 3.53/0.85 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((eq @ (pf @ (fr @ X0 @ X2) @ (fr @ X1 @ X2)) @ (fr @ (pl @ X0 @ X1) @ X2))) = $true)) )),
% 3.53/0.85 inference(cnf_transformation,[],[f24])).
% 3.53/0.85 thf(f50,plain,(
% 3.53/0.85 ( ! [X0 : frac,X1 : nat] : ((((eq @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X0)) = $true)) )),
% 3.53/0.85 inference(cnf_transformation,[],[f28])).
% 3.53/0.85 thf(f51,plain,(
% 3.53/0.85 ( ! [X0 : frac] : ((((eq @ (pf @ y @ X0) @ x)) != $true)) )),
% 3.53/0.85 inference(cnf_transformation,[],[f32])).
% 3.53/0.85 thf(f53,definition,(
% 3.53/0.85 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.53/0.85 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.53/0.85 thf(f200,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true = ((eq @ X2 @ X1))) | ($true != ((eq @ X2 @ X0))) | (((eq @ X0 @ X1)) = $false)) )),
% 3.53/0.85 inference(constrained_superposition,[],[f43,f53])).
% 3.53/0.85 thf(f208,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X2 @ X0))) | ($true = ((eq @ X2 @ X1))) | (((eq @ X0 @ X1)) = $false)) )),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f200])).
% 3.53/0.85 thf(f292,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true = ((eq @ (pf @ X1 @ X0) @ (pf @ X2 @ X0)))) | (((eq @ X1 @ X2)) != $true)) )),
% 3.53/0.85 inference(constrained_superposition,[],[f44,f46])).
% 3.53/0.85 thf(f300,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((eq @ X1 @ X2)) != $true) | ($true = ((eq @ (pf @ X1 @ X0) @ (pf @ X2 @ X0))))) )),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f292])).
% 3.53/0.85 thf(f319,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | (((eq @ X0 @ X2)) = $true) | (((eq @ X1 @ X2)) = $false) | (((eq @ X0 @ X1)) = $false)) )),
% 3.53/0.85 inference(constrained_superposition,[],[f208,f53])).
% 3.53/0.85 thf(f322,plain,(
% 3.53/0.85 ( ! [X2 : nat,X3 : frac,X0 : nat,X1 : nat] : (($true != $true) | ($true = ((eq @ (pf @ (fr @ X0 @ X1) @ (fr @ X2 @ X1)) @ X3))) | ($false = ((eq @ (fr @ (pl @ X0 @ X2) @ X1) @ X3)))) )),
% 3.53/0.85 inference(constrained_superposition,[],[f208,f48])).
% 3.53/0.85 thf(f332,plain,(
% 3.53/0.85 ( ! [X2 : nat,X3 : frac,X0 : nat,X1 : nat] : (($true = ((eq @ (pf @ (fr @ X0 @ X1) @ (fr @ X2 @ X1)) @ X3))) | ($false = ((eq @ (fr @ (pl @ X0 @ X2) @ X1) @ X3)))) )),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f322])).
% 3.53/0.85 thf(f334,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((eq @ X0 @ X2)) = $true) | (((eq @ X1 @ X2)) = $false) | (((eq @ X0 @ X1)) = $false)) )),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f319])).
% 3.53/0.85 thf(f340,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : nat] : (($true != $true) | ($true = ((eq @ (pf @ X0 @ X2) @ (pf @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X2))))) )),
% 3.53/0.85 inference(constrained_superposition,[],[f300,f45])).
% 3.53/0.85 thf(f346,plain,(
% 3.53/0.85 ( ! [X2 : frac,X0 : frac,X1 : nat] : (($true = ((eq @ (pf @ X0 @ X2) @ (pf @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X2))))) )),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f340])).
% 3.53/0.85 thf(f395,plain,(
% 3.53/0.85 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ($false = ((eq @ X1 @ x))) | ($false = ((eq @ (pf @ y @ X0) @ X1)))) )),
% 3.53/0.85 inference(constrained_superposition,[],[f51,f334])).
% 3.53/0.85 thf(f460,plain,(
% 3.53/0.85 ( ! [X0 : frac,X1 : frac] : (($false = ((eq @ (pf @ y @ X0) @ X1))) | ($false = ((eq @ X1 @ x)))) )),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f395])).
% 3.53/0.85 thf(f3468,plain,(
% 3.53/0.85 ( ! [X0 : frac,X1 : nat] : (($true = $false) | ($false = ((eq @ (pf @ (fr @ (ts @ (num @ y) @ X1) @ (ts @ (den @ y) @ X1)) @ X0) @ x)))) )),
% 3.53/0.85 inference(constrained_superposition,[],[f460,f346])).
% 3.53/0.85 thf(f3522,plain,(
% 3.53/0.85 ( ! [X0 : frac,X1 : nat] : (($false = ((eq @ (pf @ (fr @ (ts @ (num @ y) @ X1) @ (ts @ (den @ y) @ X1)) @ X0) @ x)))) )),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f3468])).
% 3.53/0.85 thf(f4682,plain,(
% 3.53/0.85 ( ! [X0 : nat,X1 : nat] : (($true = $false) | ($false = ((eq @ (fr @ (pl @ (ts @ (num @ y) @ X0) @ X1) @ (ts @ (den @ y) @ X0)) @ x)))) )),
% 3.53/0.85 inference(constrained_superposition,[],[f332,f3522])).
% 3.53/0.85 thf(f4708,plain,(
% 3.53/0.85 ( ! [X0 : nat,X1 : nat] : (($false = ((eq @ (fr @ (pl @ (ts @ (num @ y) @ X0) @ X1) @ (ts @ (den @ y) @ X0)) @ x)))) )),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f4682])).
% 3.53/0.85 thf(f6304,plain,(
% 3.53/0.85 ($false = ((eq @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ y) @ (den @ x))) @ x)))),
% 3.53/0.85 inference(constrained_superposition,[],[f4708,f41])).
% 3.53/0.85 thf(f6344,plain,(
% 3.53/0.85 ($false = ((eq @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ x) @ (den @ y))) @ x)))),
% 3.53/0.85 inference(forward_demodulation,[],[f6304,f47])).
% 3.53/0.85 thf(f6454,plain,(
% 3.53/0.85 ($true = $false)),
% 3.53/0.85 inference(constrained_superposition,[],[f50,f6344])).
% 3.53/0.85 thf(f6485,plain,(
% 3.53/0.85 $false),
% 3.53/0.85 inference(trivial_inequality_removal,[],[f6454])).
% 3.53/0.85 % SZS output end Proof for theBenchmark
% 3.53/0.85 % (28002)------------------------------
% 3.53/0.85 % (28002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.53/0.85 % (28002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/0.85 % (28002)CaDiCaL version: 2.1.3
% 3.53/0.85 % (28002)Termination reason: Refutation
% 3.53/0.85 % (28002)Time elapsed: 0.559 s
% 3.53/0.85 % (28002)Peak memory usage: 15 MB
% 3.53/0.85 % (28002)Instructions burned: 926 (million)
% 3.53/0.85 % (27981)Success in time 0.603 s
% 3.53/0.85 % Vampire exiting
%------------------------------------------------------------------------------