%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV401^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:27 AM UTC 2026
% Result : Theorem 2.55s 0.61s
% Output : Refutation 2.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV401^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 15:43:51 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 2.55/0.60 % (2275348)Will run a generic schedule for satisfiability detection.
% 2.55/0.60 % (2275353)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1749253198_2999 on theBenchmark for (2999ds/0Mi)
% 2.55/0.60 % Exception at run slice level
% 2.55/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.55/0.60 % (2275354)% WARNING: option uhcvi not known.
% 2.55/0.60 % (2275354)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3083782710:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.55/0.60 % (2275356)dis+10_1_sil=32000:sp=arity:random_seed=1353085525:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.55/0.60 % (2275355)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2371332084:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.55/0.60 % (2275357)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1167265752:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.55/0.60 % (2275359)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1140925997:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.55/0.61 % (2275354)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.55/0.61 % (2275357)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.55/0.61 % (2275354)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.55/0.61 % (2275358)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=674877106:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.55/0.61 % (2275361)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3789272194:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.55/0.61 % Exception at run slice level
% 2.55/0.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.55/0.61 % (2275369)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2665000489:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.55/0.61 % (2275359)Instruction limit reached!
% 2.55/0.61 % (2275359)------------------------------
% 2.55/0.61 % (2275359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275359)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275359)Termination reason: Instruction limit
% 2.55/0.61 % (2275359)Termination phase: Saturation
% 2.55/0.61 % (2275359)Time elapsed: 0.043 s
% 2.55/0.61 % (2275359)Peak memory usage: 12 MB
% 2.55/0.61 % (2275359)Instructions burned: 162 (million)
% 2.55/0.61 % (2275356)Instruction limit reached!
% 2.55/0.61 % (2275356)------------------------------
% 2.55/0.61 % (2275356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275356)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275356)Termination reason: Instruction limit
% 2.55/0.61 % (2275356)Termination phase: Saturation
% 2.55/0.61 % (2275356)Time elapsed: 0.052 s
% 2.55/0.61 % (2275356)Peak memory usage: 12 MB
% 2.55/0.61 % (2275356)Instructions burned: 103 (million)
% 2.55/0.61 % (2275371)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=2902576844:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.55/0.61 % (2275371)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.55/0.61 % (2275371)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.55/0.61 % (2275357)Instruction limit reached!
% 2.55/0.61 % (2275357)------------------------------
% 2.55/0.61 % (2275357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275357)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275357)Termination reason: Instruction limit
% 2.55/0.61 % (2275357)Termination phase: Saturation
% 2.55/0.61 % (2275357)Time elapsed: 0.058 s
% 2.55/0.61 % (2275357)Peak memory usage: 12 MB
% 2.55/0.61 % (2275357)Instructions burned: 118 (million)
% 2.55/0.61 % (2275358)Instruction limit reached!
% 2.55/0.61 % (2275358)------------------------------
% 2.55/0.61 % (2275358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275358)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275358)Termination reason: Instruction limit
% 2.55/0.61 % (2275358)Termination phase: Saturation
% 2.55/0.61 % (2275358)Time elapsed: 0.065 s
% 2.55/0.61 % (2275358)Peak memory usage: 12 MB
% 2.55/0.61 % (2275358)Instructions burned: 132 (million)
% 2.55/0.61 % (2275372)ott-21_1_sil=16000:fs=off:random_seed=943378976:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.55/0.61 % (2275374)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1583241378:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 2.55/0.61 % (2275375)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=722630756:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.55/0.61 % Exception at run slice level
% 2.55/0.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.55/0.61 % (2275379)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=928760361:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.55/0.61 % (2275369)Instruction limit reached!
% 2.55/0.61 % (2275369)------------------------------
% 2.55/0.61 % (2275369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275369)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275369)Termination reason: Instruction limit
% 2.55/0.61 % (2275369)Termination phase: Saturation
% 2.55/0.61 % (2275369)Time elapsed: 0.099 s
% 2.55/0.61 % (2275369)Peak memory usage: 12 MB
% 2.55/0.61 % (2275369)Instructions burned: 132 (million)
% 2.55/0.61 % (2275372)Instruction limit reached!
% 2.55/0.61 % (2275372)------------------------------
% 2.55/0.61 % (2275372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275372)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275372)Termination reason: Instruction limit
% 2.55/0.61 % (2275372)Termination phase: Saturation
% 2.55/0.61 % (2275372)Time elapsed: 0.085 s
% 2.55/0.61 % (2275372)Peak memory usage: 12 MB
% 2.55/0.61 % (2275372)Instructions burned: 181 (million)
% 2.55/0.61 % (2275381)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3679364720:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.55/0.61 % Exception at run slice level
% 2.55/0.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.55/0.61 % (2275382)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=891434800: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)
% 2.55/0.61 % (2275382)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.55/0.61 % (2275384)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2029872134:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.55/0.61 % (2275384)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.55/0.61 % (2275371)Instruction limit reached!
% 2.55/0.61 % (2275371)------------------------------
% 2.55/0.61 % (2275371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275371)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275371)Termination reason: Instruction limit
% 2.55/0.61 % (2275371)Termination phase: Saturation
% 2.55/0.61 % (2275371)Time elapsed: 0.167 s
% 2.55/0.61 % (2275371)Peak memory usage: 15 MB
% 2.55/0.61 % (2275371)Instructions burned: 684 (million)
% 2.55/0.61 % (2275387)fmb+10_1_sil=64000:random_seed=1371099375:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.55/0.61 % (2275387)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.55/0.61 % Exception at run slice level
% 2.55/0.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.55/0.61 % (2275389)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=290359828:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 2.55/0.61 % Exception at run slice level
% 2.55/0.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.55/0.61 % (2275391)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=388306547:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 2.55/0.61 % Exception at run slice level
% 2.55/0.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.55/0.61 % (2275393)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3189426429:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 2.55/0.61 % (2275393)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.55/0.61 % (2275374)Instruction limit reached!
% 2.55/0.61 % (2275374)------------------------------
% 2.55/0.61 % (2275374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275374)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275374)Termination reason: Instruction limit
% 2.55/0.61 % (2275374)Termination phase: Saturation
% 2.55/0.61 % (2275374)Time elapsed: 0.240 s
% 2.55/0.61 % (2275374)Peak memory usage: 13 MB
% 2.55/0.61 % (2275374)Instructions burned: 478 (million)
% 2.55/0.61 % (2275395)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=170738991:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 2.55/0.61 % (2275395)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.55/0.61 % (2275395)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.55/0.61 % (2275393) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2275348-2275393"...
% 2.55/0.61 % (2275393)...printing done.
% 2.55/0.61 % (2275393)Refutation found. Thanks to Tanya!
% 2.55/0.61 % SZS status Theorem for theBenchmark
% 2.55/0.61 % SZS output start Proof for theBenchmark
% 2.55/0.61 thf(type_def_5, type, a: $tType).
% 2.55/0.61 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 2.55/0.61 thf(func_def_0, type, cF: ((a > $o) > a > $o)).
% 2.55/0.61 thf(func_def_1, type, cG: ((a > $o) > a > $o)).
% 2.55/0.61 thf(func_def_5, type, sK0: (a > $o)).
% 2.55/0.61 thf(func_def_6, type, sK1: a).
% 2.55/0.61 thf(func_def_7, type, sK2: ((a > $o) > (a > $o) > a)).
% 2.55/0.61 thf(func_def_8, type, vNOT: ($o > $o)).
% 2.55/0.61 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 2.55/0.61 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.55/0.61 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 2.55/0.61 thf(func_def_13, type, sK4: (a > (a > a > $o) > a)).
% 2.55/0.61 thf(func_def_14, type, db2: !>[X0: $tType]:(X0)).
% 2.55/0.61 thf(func_def_15, type, sK5: ((a > $o) > a)).
% 2.55/0.61 thf(f1,conjecture,(
% 2.55/0.61 (! [X0 : (a > $o),X2 : a] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2)) & ! [X0 : (a > $o),X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2)) & ! [X0 : (a > $o),X1 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cF @ X1 @ X2) => (cF @ X0 @ X2)))) => ! [X0 : (a > $o),X2 : a] : ((cF @ (cG @ (cF @ X0)) @ X2) <=> (cF @ X0 @ X2))),
% 2.55/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM67_pme)).
% 2.55/0.61 thf(f2,negated_conjecture,(
% 2.55/0.61 ~((! [X0 : (a > $o),X2 : a] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2)) & ! [X0 : (a > $o),X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2)) & ! [X0 : (a > $o),X1 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cF @ X1 @ X2) => (cF @ X0 @ X2)))) => ! [X0 : (a > $o),X2 : a] : ((cF @ (cG @ (cF @ X0)) @ X2) <=> (cF @ X0 @ X2)))),
% 2.55/0.61 inference(negated_conjecture,[status(cth)],[f1])).
% 2.55/0.61 thf(f3,plain,(
% 2.55/0.61 ~((! [X0 : (a > $o),X1 : a] : ((X0 @ X1) => (cG @ (cF @ X0) @ X1)) & ! [X2 : (a > $o),X3 : a] : ((X2 @ X3) => (cF @ (cG @ X2) @ X3)) & ! [X4 : (a > $o),X5 : (a > $o)] : (! [X6 : a] : ((X4 @ X6) => (X5 @ X6)) => ! [X7 : a] : ((cF @ X5 @ X7) => (cF @ X4 @ X7)))) => ! [X8 : (a > $o),X9 : a] : ((cF @ (cG @ (cF @ X8)) @ X9) <=> (cF @ X8 @ X9)))),
% 2.55/0.61 inference(rectify,[],[f2])).
% 2.55/0.61 thf(f4,plain,(
% 2.55/0.61 ~((! [X0 : (a > $o),X1 : a] : ((((X0 @ X1)) = $true) => (((cG @ (cF @ X0) @ X1)) = $true)) & ! [X2 : (a > $o),X3 : a] : ((((X2 @ X3)) = $true) => (((cF @ (cG @ X2) @ X3)) = $true)) & ! [X4 : (a > $o),X5 : (a > $o)] : (! [X6 : a] : ((((X4 @ X6)) = $true) => (((X5 @ X6)) = $true)) => ! [X7 : a] : ((((cF @ X5 @ X7)) = $true) => (((cF @ X4 @ X7)) = $true)))) => ! [X8 : (a > $o),X9 : a] : (((cF @ (cG @ (cF @ X8)) @ X9)) = ((cF @ X8 @ X9))))),
% 2.55/0.61 inference(fool_elimination,[],[f3])).
% 2.55/0.61 thf(f5,plain,(
% 2.55/0.61 ? [X8 : (a > $o),X9 : a] : (((cF @ (cG @ (cF @ X8)) @ X9)) != ((cF @ X8 @ X9))) & (! [X0 : (a > $o),X1 : a] : ((((cG @ (cF @ X0) @ X1)) = $true) | (((X0 @ X1)) != $true)) & ! [X2 : (a > $o),X3 : a] : ((((cF @ (cG @ X2) @ X3)) = $true) | (((X2 @ X3)) != $true)) & ! [X4 : (a > $o),X5 : (a > $o)] : (! [X7 : a] : ((((cF @ X4 @ X7)) = $true) | (((cF @ X5 @ X7)) != $true)) | ? [X6 : a] : ((((X5 @ X6)) != $true) & (((X4 @ X6)) = $true))))),
% 2.55/0.61 inference(ennf_transformation,[],[f4])).
% 2.55/0.61 thf(f6,plain,(
% 2.55/0.61 ? [X8 : (a > $o),X9 : a] : (((cF @ (cG @ (cF @ X8)) @ X9)) != ((cF @ X8 @ X9))) & ! [X0 : (a > $o),X1 : a] : ((((cG @ (cF @ X0) @ X1)) = $true) | (((X0 @ X1)) != $true)) & ! [X2 : (a > $o),X3 : a] : ((((cF @ (cG @ X2) @ X3)) = $true) | (((X2 @ X3)) != $true)) & ! [X4 : (a > $o),X5 : (a > $o)] : (! [X7 : a] : ((((cF @ X4 @ X7)) = $true) | (((cF @ X5 @ X7)) != $true)) | ? [X6 : a] : ((((X5 @ X6)) != $true) & (((X4 @ X6)) = $true)))),
% 2.55/0.61 inference(flattening,[],[f5])).
% 2.55/0.61 thf(f7,plain,(
% 2.55/0.61 ? [X0 : (a > $o),X1 : a] : (((cF @ (cG @ (cF @ X0)) @ X1)) != ((cF @ X0 @ X1))) & ! [X2 : (a > $o),X3 : a] : (($true = ((cG @ (cF @ X2) @ X3))) | (((X2 @ X3)) != $true)) & ! [X4 : (a > $o),X5 : a] : (($true = ((cF @ (cG @ X4) @ X5))) | ($true != ((X4 @ X5)))) & ! [X6 : (a > $o),X7 : (a > $o)] : (! [X8 : a] : (($true = ((cF @ X6 @ X8))) | ($true != ((cF @ X7 @ X8)))) | ? [X9 : a] : (($true != ((X7 @ X9))) & ($true = ((X6 @ X9)))))),
% 2.55/0.61 inference(rectify,[],[f6])).
% 2.55/0.61 thf(f8,plain,(
% 2.55/0.61 (((cF @ (cG @ (cF @ sK0)) @ sK1)) != ((cF @ sK0 @ sK1))) & ! [X2 : (a > $o),X3 : a] : (($true = ((cG @ (cF @ X2) @ X3))) | (((X2 @ X3)) != $true)) & ! [X4 : (a > $o),X5 : a] : (($true = ((cF @ (cG @ X4) @ X5))) | ($true != ((X4 @ X5)))) & ! [X6 : (a > $o),X7 : (a > $o)] : (! [X8 : a] : (($true = ((cF @ X6 @ X8))) | ($true != ((cF @ X7 @ X8)))) | (($true != ((X7 @ (sK2 @ X7 @ X6)))) & ($true = ((X6 @ (sK2 @ X7 @ X6))))))),
% 2.55/0.61 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X9,sK2 @ X7 @ X6)],[f7])).
% 2.55/0.61 thf(f9,plain,(
% 2.55/0.61 ( ! [X8 : a,X6 : (a > $o),X7 : (a > $o)] : (($true != ((cF @ X7 @ X8))) | ($true = ((cF @ X6 @ X8))) | ($true = ((X6 @ (sK2 @ X7 @ X6))))) )),
% 2.55/0.61 inference(cnf_transformation,[],[f8])).
% 2.55/0.61 thf(f10,plain,(
% 2.55/0.61 ( ! [X8 : a,X6 : (a > $o),X7 : (a > $o)] : (($true != ((cF @ X7 @ X8))) | ($true = ((cF @ X6 @ X8))) | ($true != ((X7 @ (sK2 @ X7 @ X6))))) )),
% 2.55/0.61 inference(cnf_transformation,[],[f8])).
% 2.55/0.61 thf(f11,plain,(
% 2.55/0.61 ( ! [X4 : (a > $o),X5 : a] : (($true != ((X4 @ X5))) | ($true = ((cF @ (cG @ X4) @ X5)))) )),
% 2.55/0.61 inference(cnf_transformation,[],[f8])).
% 2.55/0.61 thf(f12,plain,(
% 2.55/0.61 ( ! [X2 : (a > $o),X3 : a] : ((((X2 @ X3)) != $true) | ($true = ((cG @ (cF @ X2) @ X3)))) )),
% 2.55/0.61 inference(cnf_transformation,[],[f8])).
% 2.55/0.61 thf(f13,plain,(
% 2.55/0.61 (((cF @ (cG @ (cF @ sK0)) @ sK1)) != ((cF @ sK0 @ sK1)))),
% 2.55/0.61 inference(cnf_transformation,[],[f8])).
% 2.55/0.61 thf(f15,definition,(
% 2.55/0.61 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.55/0.61 introduced(theory,[fool_exhaustiveness_axiom])).
% 2.55/0.61 thf(f16,plain,(
% 2.55/0.61 ($true = ((cF @ (cG @ (cF @ sK0)) @ sK1))) | ($true = ((cF @ sK0 @ sK1)))),
% 2.55/0.61 inference(xor_proxy_clausification,[],[f13])).
% 2.55/0.61 thf(f17,plain,(
% 2.55/0.61 (((cF @ (cG @ (cF @ sK0)) @ sK1)) = $false) | (((cF @ sK0 @ sK1)) = $false)),
% 2.55/0.61 inference(xor_proxy_clausification,[],[f13])).
% 2.55/0.61 thf(f56,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | (((cG @ (cF @ X0) @ X1)) = $true) | (((X0 @ X1)) = $false)) )),
% 2.55/0.61 inference(constrained_superposition,[],[f12,f15])).
% 2.55/0.61 thf(f64,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o),X1 : a] : ((((cG @ (cF @ X0) @ X1)) = $true) | (((X0 @ X1)) = $false)) )),
% 2.55/0.61 inference(trivial_inequality_removal,[],[f56])).
% 2.55/0.61 thf(f121,plain,(
% 2.55/0.61 ($true = ((cF @ (cG @ (cF @ sK0)) @ sK1)))),
% 2.55/0.61 inference(forward_subsumption_resolution,[],[f16,f11])).
% 2.55/0.61 thf(f126,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((cF @ X0 @ sK1))) | ($true != ((cG @ (cF @ sK0) @ (sK2 @ (cG @ (cF @ sK0)) @ X0))))) )),
% 2.55/0.61 inference(constrained_superposition,[],[f10,f121])).
% 2.55/0.61 thf(f127,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((cF @ X0 @ sK1))) | ($true = ((X0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0))))) )),
% 2.55/0.61 inference(constrained_superposition,[],[f9,f121])).
% 2.55/0.61 thf(f128,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true = ((X0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0)))) | ($true = ((cF @ X0 @ sK1)))) )),
% 2.55/0.61 inference(trivial_inequality_removal,[],[f127])).
% 2.55/0.61 thf(f129,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true != ((cG @ (cF @ sK0) @ (sK2 @ (cG @ (cF @ sK0)) @ X0)))) | ($true = ((cF @ X0 @ sK1)))) )),
% 2.55/0.61 inference(trivial_inequality_removal,[],[f126])).
% 2.55/0.61 thf(f139,definition,(
% 2.55/0.61 spl3_1 <=> (((cF @ sK0 @ sK1)) = $false)),
% 2.55/0.61 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 2.55/0.61 thf(f141,plain,(
% 2.55/0.61 (((cF @ sK0 @ sK1)) = $false) | ~spl3_1),
% 2.55/0.61 inference(avatar_component_clause,[],[f139])).
% 2.55/0.61 thf(f143,definition,(
% 2.55/0.61 spl3_2 <=> (((cF @ (cG @ (cF @ sK0)) @ sK1)) = $false)),
% 2.55/0.61 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 2.55/0.61 thf(f145,plain,(
% 2.55/0.61 (((cF @ (cG @ (cF @ sK0)) @ sK1)) = $false) | ~spl3_2),
% 2.55/0.61 inference(avatar_component_clause,[],[f143])).
% 2.55/0.61 thf(f146,plain,(
% 2.55/0.61 spl3_1 | spl3_2),
% 2.55/0.61 inference(avatar_split_clause,[],[f17,f143,f139])).
% 2.55/0.61 thf(f148,plain,(
% 2.55/0.61 ($true = $false) | ~spl3_2),
% 2.55/0.61 inference(constrained_superposition,[],[f145,f121])).
% 2.55/0.61 thf(f166,plain,(
% 2.55/0.61 $false | ~spl3_2),
% 2.55/0.61 inference(trivial_inequality_removal,[],[f148])).
% 2.55/0.61 thf(f167,plain,(
% 2.55/0.61 ~spl3_2),
% 2.55/0.61 inference(avatar_contradiction_clause,[],[f166])).
% 2.55/0.61 thf(f2140,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((cF @ X0 @ sK1))) | ($false = ((sK0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0))))) )),
% 2.55/0.61 inference(constrained_superposition,[],[f129,f64])).
% 2.55/0.61 thf(f2188,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($false = ((sK0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0)))) | ($true = ((cF @ X0 @ sK1)))) )),
% 2.55/0.61 inference(trivial_inequality_removal,[],[f2140])).
% 2.55/0.61 thf(f2215,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true = $false) | ($true = ((cF @ (^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK1))) | ($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) )),
% 2.55/0.61 inference(constrained_superposition,[],[f128,f2188])).
% 2.55/0.61 thf(f2236,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true = ((cF @ (^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK1))) | ($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) )),
% 2.55/0.61 inference(trivial_inequality_removal,[],[f2215])).
% 2.55/0.61 thf(f2237,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true = ((cF @ sK0 @ sK1))) | ($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) )),
% 2.55/0.61 inference(beta-eta_normalization,[],[f2236])).
% 2.55/0.61 thf(f2283,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : (($true = $false) | ($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) ) | ~spl3_1),
% 2.55/0.61 inference(forward_demodulation,[],[f2237,f141])).
% 2.55/0.61 thf(f2284,plain,(
% 2.55/0.61 ( ! [X0 : (a > $o)] : ((sK0 != X0) | ($true = ((cF @ X0 @ sK1)))) ) | ~spl3_1),
% 2.55/0.61 inference(trivial_inequality_removal,[],[f2283])).
% 2.55/0.61 thf(f2295,plain,(
% 2.55/0.61 ($true = ((cF @ sK0 @ sK1))) | ~spl3_1),
% 2.55/0.61 inference(equality_resolution,[],[f2284])).
% 2.55/0.61 thf(f2298,plain,(
% 2.55/0.61 ($true = $false) | ~spl3_1),
% 2.55/0.61 inference(forward_demodulation,[],[f2295,f141])).
% 2.55/0.61 thf(f2299,plain,(
% 2.55/0.61 $false | ~spl3_1),
% 2.55/0.61 inference(trivial_inequality_removal,[],[f2298])).
% 2.55/0.61 thf(f2300,plain,(
% 2.55/0.61 ~spl3_1),
% 2.55/0.61 inference(avatar_contradiction_clause,[],[f2299])).
% 2.55/0.61 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f146])).
% 2.55/0.61 cnf(s3, plain, ~spl3_2, inference(sat_conversion,[],[f167])).
% 2.55/0.61 cnf(s4, plain, ~spl3_1, inference(sat_conversion,[],[f2300])).
% 2.55/0.61 cnf(s5, plain, $false, inference(rat,[],[s1,s3,s4])).
% 2.55/0.61 thf(f2301,plain,(
% 2.55/0.61 $false),
% 2.55/0.61 inference(avatar_sat_refutation,[],[s5])).
% 2.55/0.61 % SZS output end Proof for theBenchmark
% 2.55/0.61 % (2275393)------------------------------
% 2.55/0.61 % (2275393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.61 % (2275393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.61 % (2275393)CaDiCaL version: 2.1.3
% 2.55/0.61 % (2275393)Termination reason: Refutation
% 2.55/0.61 % (2275393)Time elapsed: 0.079 s
% 2.55/0.61 % (2275393)Peak memory usage: 14 MB
% 2.55/0.61 % (2275393)Instructions burned: 317 (million)
% 2.55/0.61 % (2275348)Success in time 0.386 s
% 2.55/0.61 % Vampire exiting
%------------------------------------------------------------------------------