%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU974^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:34:29 AM UTC 2026
% Result : Theorem 0.89s 0.46s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU974^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:54:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.89/0.46 % (1769189)Will run a generic schedule for satisfiability detection.
% 0.89/0.46 % (1769206)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3482235109:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.89/0.46 % (1769208)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1137829762:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.89/0.46 % (1769207)dis+10_1_sil=32000:sp=arity:random_seed=3859537857:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.89/0.46 % (1769210)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1560401837:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.89/0.46 % (1769208)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.89/0.46 % (1769205)% WARNING: option uhcvi not known.
% 0.89/0.46 % (1769204)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3573985743_2999 on theBenchmark for (2999ds/0Mi)
% 0.89/0.46 % (1769205)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2433985733:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.89/0.46 % Exception at run slice level
% 0.89/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.89/0.46 % (1769205)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.89/0.46 % (1769205)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.89/0.46 % (1769209)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4020194578:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.89/0.46 % (1769217)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1874365556:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.89/0.46 % Exception at run slice level
% 0.89/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.89/0.46 % (1769207)Instruction limit reached!
% 0.89/0.46 % (1769207)------------------------------
% 0.89/0.46 % (1769207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.46 % (1769207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.46 % (1769207)CaDiCaL version: 2.1.3
% 0.89/0.46 % (1769207)Termination reason: Instruction limit
% 0.89/0.46 % (1769207)Termination phase: Saturation
% 0.89/0.46 % (1769207)Time elapsed: 0.051 s
% 0.89/0.46 % (1769207)Peak memory usage: 12 MB
% 0.89/0.46 % (1769207)Instructions burned: 103 (million)
% 0.89/0.46 % (1769221)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1381380706:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.89/0.46 % (1769222)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=4190844855:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.89/0.46 % (1769222)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.89/0.46 % (1769222)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.89/0.46 % (1769208)Instruction limit reached!
% 0.89/0.46 % (1769208)------------------------------
% 0.89/0.46 % (1769208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.46 % (1769208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.46 % (1769208)CaDiCaL version: 2.1.3
% 0.89/0.46 % (1769208)Termination reason: Instruction limit
% 0.89/0.46 % (1769208)Termination phase: Saturation
% 0.89/0.46 % (1769208)Time elapsed: 0.079 s
% 0.89/0.46 % (1769208)Peak memory usage: 12 MB
% 0.89/0.46 % (1769208)Instructions burned: 118 (million)
% 0.89/0.46 % (1769210)Instruction limit reached!
% 0.89/0.46 % (1769210)------------------------------
% 0.89/0.46 % (1769210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.46 % (1769210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.46 % (1769210)CaDiCaL version: 2.1.3
% 0.89/0.46 % (1769210)Termination reason: Instruction limit
% 0.89/0.46 % (1769210)Termination phase: Saturation
% 0.89/0.46 % (1769210)Time elapsed: 0.085 s
% 0.89/0.46 % (1769210)Peak memory usage: 13 MB
% 0.89/0.46 % (1769210)Instructions burned: 160 (million)
% 0.89/0.46 % (1769225)ott-21_1_sil=16000:fs=off:random_seed=1974345327:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.89/0.46 % (1769226)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=364450945:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.89/0.46 % (1769209)Instruction limit reached!
% 0.89/0.46 % (1769209)------------------------------
% 0.89/0.46 % (1769209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.46 % (1769209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.46 % (1769209)CaDiCaL version: 2.1.3
% 0.89/0.46 % (1769209)Termination reason: Instruction limit
% 0.89/0.46 % (1769209)Termination phase: Saturation
% 0.89/0.46 % (1769209)Time elapsed: 0.114 s
% 0.89/0.46 % (1769209)Peak memory usage: 12 MB
% 0.89/0.46 % (1769209)Instructions burned: 131 (million)
% 0.89/0.46 % (1769221)Instruction limit reached!
% 0.89/0.46 % (1769221)------------------------------
% 0.89/0.46 % (1769221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.46 % (1769221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.46 % (1769221)CaDiCaL version: 2.1.3
% 0.89/0.46 % (1769221)Termination reason: Instruction limit
% 0.89/0.46 % (1769221)Termination phase: Saturation
% 0.89/0.46 % (1769221)Time elapsed: 0.070 s
% 0.89/0.46 % (1769221)Peak memory usage: 12 MB
% 0.89/0.46 % (1769221)Instructions burned: 131 (million)
% 0.89/0.46 % (1769230)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4069120140:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.89/0.46 % (1769229)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1088259856:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.89/0.46 % Exception at run slice level
% 0.89/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.89/0.46 % (1769225)Instruction limit reached!
% 0.89/0.46 % (1769225)------------------------------
% 0.89/0.46 % (1769225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.46 % (1769225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.46 % (1769225)CaDiCaL version: 2.1.3
% 0.89/0.46 % (1769225)Termination reason: Instruction limit
% 0.89/0.46 % (1769225)Termination phase: Saturation
% 0.89/0.46 % (1769225)Time elapsed: 0.082 s
% 0.89/0.46 % (1769225)Peak memory usage: 12 MB
% 0.89/0.46 % (1769225)Instructions burned: 180 (million)
% 0.89/0.46 % (1769222) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1769189-1769222"...
% 0.89/0.46 % (1769222)...printing done.
% 0.89/0.46 % (1769222)Refutation found. Thanks to Tanya!
% 0.89/0.46 % SZS status Theorem for theBenchmark
% 0.89/0.46 % SZS output start Proof for theBenchmark
% 0.89/0.46 thf(type_def_5, type, a: $tType).
% 0.89/0.46 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.89/0.46 thf(func_def_0, type, cR: (a > a)).
% 0.89/0.46 thf(func_def_1, type, cP: (a > a > a)).
% 0.89/0.46 thf(func_def_2, type, cL: (a > a)).
% 0.89/0.46 thf(func_def_3, type, cZ: a).
% 0.89/0.46 thf(func_def_7, type, sK0: a).
% 0.89/0.46 thf(func_def_8, type, sK1: a).
% 0.89/0.46 thf(func_def_9, type, sK2: ((a > $o) > a)).
% 0.89/0.46 thf(func_def_10, type, sK3: ((a > $o) > a)).
% 0.89/0.46 thf(func_def_11, type, sK4: (a > $o)).
% 0.89/0.46 thf(func_def_12, type, sK5: ((a > $o) > a)).
% 0.89/0.46 thf(func_def_13, type, sK6: ((a > $o) > a)).
% 0.89/0.46 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.89/0.46 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.89/0.46 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.89/0.46 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.89/0.46 thf(f1,conjecture,(
% 0.89/0.46 (! [X3 : (a > $o)] : (! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))) & ((X2 = cZ) <=> (X4 = cZ)))) => ! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => (X2 = X4))) & ! [X2 : a] : ((X2 != cZ) <=> (X2 = ((cP @ (cL @ X2) @ (cR @ X2))))) & ! [X0 : a,X1 : a] : (((cR @ (cP @ X0 @ X1))) = X1) & ! [X0 : a,X1 : a] : (((cL @ (cP @ X0 @ X1))) = X0) & (((cR @ cZ)) = cZ) & (((cL @ cZ)) = cZ)) => ! [X0 : a,X1 : a] : (? [X3 : (a > $o)] : (! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))) & ((X4 = cZ) => (X2 = cZ)))) & (X3 @ (cP @ X0 @ X1))) => ? [X3 : (a > $o)] : (! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))) & ((X4 = cZ) => (X2 = cZ)))) & (X3 @ (cP @ (cR @ X0) @ (cR @ X1)))))),
% 0.89/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPU_LEM2C_pme)).
% 0.89/0.46 thf(f2,negated_conjecture,(
% 0.89/0.46 ~((! [X3 : (a > $o)] : (! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))) & ((X2 = cZ) <=> (X4 = cZ)))) => ! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => (X2 = X4))) & ! [X2 : a] : ((X2 != cZ) <=> (X2 = ((cP @ (cL @ X2) @ (cR @ X2))))) & ! [X0 : a,X1 : a] : (((cR @ (cP @ X0 @ X1))) = X1) & ! [X0 : a,X1 : a] : (((cL @ (cP @ X0 @ X1))) = X0) & (((cR @ cZ)) = cZ) & (((cL @ cZ)) = cZ)) => ! [X0 : a,X1 : a] : (? [X3 : (a > $o)] : (! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))) & ((X4 = cZ) => (X2 = cZ)))) & (X3 @ (cP @ X0 @ X1))) => ? [X3 : (a > $o)] : (! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))) & ((X4 = cZ) => (X2 = cZ)))) & (X3 @ (cP @ (cR @ X0) @ (cR @ X1))))))),
% 0.89/0.46 inference(negated_conjecture,[status(cth)],[f1])).
% 0.89/0.46 thf(f3,plain,(
% 0.89/0.46 ~((! [X0 : (a > $o)] : (! [X1 : a,X2 : a] : ((X0 @ (cP @ X1 @ X2)) => ((X0 @ (cP @ (cR @ X1) @ (cR @ X2))) & (X0 @ (cP @ (cL @ X1) @ (cL @ X2))) & ((cZ = X1) <=> (cZ = X2)))) => ! [X3 : a,X4 : a] : ((X0 @ (cP @ X3 @ X4)) => (X3 = X4))) & ! [X5 : a] : ((cZ != X5) <=> (((cP @ (cL @ X5) @ (cR @ X5))) = X5)) & ! [X6 : a,X7 : a] : (((cR @ (cP @ X6 @ X7))) = X7) & ! [X8 : a,X9 : a] : (((cL @ (cP @ X8 @ X9))) = X8) & (((cR @ cZ)) = cZ) & (((cL @ cZ)) = cZ)) => ! [X10 : a,X11 : a] : (? [X12 : (a > $o)] : (! [X13 : a,X14 : a] : ((X12 @ (cP @ X13 @ X14)) => ((X12 @ (cP @ (cR @ X13) @ (cR @ X14))) & (X12 @ (cP @ (cL @ X13) @ (cL @ X14))) & ((cZ = X14) => (cZ = X13)))) & (X12 @ (cP @ X10 @ X11))) => ? [X15 : (a > $o)] : (! [X16 : a,X17 : a] : ((X15 @ (cP @ X16 @ X17)) => ((X15 @ (cP @ (cR @ X16) @ (cR @ X17))) & (X15 @ (cP @ (cL @ X16) @ (cL @ X17))) & ((cZ = X17) => (cZ = X16)))) & (X15 @ (cP @ (cR @ X10) @ (cR @ X11))))))),
% 0.89/0.46 inference(rectify,[],[f2])).
% 0.89/0.46 thf(f4,plain,(
% 0.89/0.46 ~((! [X0 : (a > $o)] : (! [X1 : a,X2 : a] : ((((X0 @ (cP @ X1 @ X2))) = $true) => ((((X0 @ (cP @ (cR @ X1) @ (cR @ X2)))) = $true) & (((X0 @ (cP @ (cL @ X1) @ (cL @ X2)))) = $true) & ((cZ = X1) <=> (cZ = X2)))) => ! [X3 : a,X4 : a] : ((((X0 @ (cP @ X3 @ X4))) = $true) => (X3 = X4))) & ! [X5 : a] : ((cZ != X5) <=> (((cP @ (cL @ X5) @ (cR @ X5))) = X5)) & ! [X6 : a,X7 : a] : (((cR @ (cP @ X6 @ X7))) = X7) & ! [X8 : a,X9 : a] : (((cL @ (cP @ X8 @ X9))) = X8) & (cZ = ((cR @ cZ))) & (cZ = ((cL @ cZ)))) => ! [X10 : a,X11 : a] : (? [X12 : (a > $o)] : (! [X13 : a,X14 : a] : ((((X12 @ (cP @ X13 @ X14))) = $true) => ((((X12 @ (cP @ (cR @ X13) @ (cR @ X14)))) = $true) & (((X12 @ (cP @ (cL @ X13) @ (cL @ X14)))) = $true) & ((cZ = X14) => (cZ = X13)))) & (((X12 @ (cP @ X10 @ X11))) = $true)) => ? [X15 : (a > $o)] : (! [X16 : a,X17 : a] : ((((X15 @ (cP @ X16 @ X17))) = $true) => ((((X15 @ (cP @ (cR @ X16) @ (cR @ X17)))) = $true) & (((X15 @ (cP @ (cL @ X16) @ (cL @ X17)))) = $true) & ((cZ = X17) => (cZ = X16)))) & (((X15 @ (cP @ (cR @ X10) @ (cR @ X11)))) = $true))))),
% 0.89/0.46 inference(fool_elimination,[],[f3])).
% 0.89/0.46 thf(f5,plain,(
% 0.89/0.46 ? [X10 : a,X11 : a] : (! [X15 : (a > $o)] : (? [X16 : a,X17 : a] : (((((X15 @ (cP @ (cR @ X16) @ (cR @ X17)))) != $true) | (((X15 @ (cP @ (cL @ X16) @ (cL @ X17)))) != $true) | ((cZ != X16) & (cZ = X17))) & (((X15 @ (cP @ X16 @ X17))) = $true)) | (((X15 @ (cP @ (cR @ X10) @ (cR @ X11)))) != $true)) & ? [X12 : (a > $o)] : (! [X13 : a,X14 : a] : (((((X12 @ (cP @ (cR @ X13) @ (cR @ X14)))) = $true) & (((X12 @ (cP @ (cL @ X13) @ (cL @ X14)))) = $true) & ((cZ = X13) | (cZ != X14))) | (((X12 @ (cP @ X13 @ X14))) != $true)) & (((X12 @ (cP @ X10 @ X11))) = $true))) & (! [X0 : (a > $o)] : (! [X3 : a,X4 : a] : ((X3 = X4) | (((X0 @ (cP @ X3 @ X4))) != $true)) | ? [X1 : a,X2 : a] : (((((X0 @ (cP @ (cR @ X1) @ (cR @ X2)))) != $true) | (((X0 @ (cP @ (cL @ X1) @ (cL @ X2)))) != $true) | ((cZ = X1) <~> (cZ = X2))) & (((X0 @ (cP @ X1 @ X2))) = $true))) & ! [X5 : a] : ((cZ != X5) <=> (((cP @ (cL @ X5) @ (cR @ X5))) = X5)) & ! [X6 : a,X7 : a] : (((cR @ (cP @ X6 @ X7))) = X7) & ! [X8 : a,X9 : a] : (((cL @ (cP @ X8 @ X9))) = X8) & (cZ = ((cR @ cZ))) & (cZ = ((cL @ cZ))))),
% 0.89/0.46 inference(ennf_transformation,[],[f4])).
% 0.89/0.46 thf(f6,plain,(
% 0.89/0.46 ? [X10 : a,X11 : a] : (! [X15 : (a > $o)] : (? [X16 : a,X17 : a] : (((((X15 @ (cP @ (cR @ X16) @ (cR @ X17)))) != $true) | (((X15 @ (cP @ (cL @ X16) @ (cL @ X17)))) != $true) | ((cZ != X16) & (cZ = X17))) & (((X15 @ (cP @ X16 @ X17))) = $true)) | (((X15 @ (cP @ (cR @ X10) @ (cR @ X11)))) != $true)) & ? [X12 : (a > $o)] : (! [X13 : a,X14 : a] : (((((X12 @ (cP @ (cR @ X13) @ (cR @ X14)))) = $true) & (((X12 @ (cP @ (cL @ X13) @ (cL @ X14)))) = $true) & ((cZ = X13) | (cZ != X14))) | (((X12 @ (cP @ X13 @ X14))) != $true)) & (((X12 @ (cP @ X10 @ X11))) = $true))) & ! [X0 : (a > $o)] : (! [X3 : a,X4 : a] : ((X3 = X4) | (((X0 @ (cP @ X3 @ X4))) != $true)) | ? [X1 : a,X2 : a] : (((((X0 @ (cP @ (cR @ X1) @ (cR @ X2)))) != $true) | (((X0 @ (cP @ (cL @ X1) @ (cL @ X2)))) != $true) | ((cZ = X1) <~> (cZ = X2))) & (((X0 @ (cP @ X1 @ X2))) = $true))) & ! [X5 : a] : ((cZ != X5) <=> (((cP @ (cL @ X5) @ (cR @ X5))) = X5)) & ! [X6 : a,X7 : a] : (((cR @ (cP @ X6 @ X7))) = X7) & ! [X8 : a,X9 : a] : (((cL @ (cP @ X8 @ X9))) = X8) & (cZ = ((cR @ cZ))) & (cZ = ((cL @ cZ)))),
% 0.89/0.46 inference(flattening,[],[f5])).
% 0.89/0.46 thf(f7,plain,(
% 0.89/0.46 ? [X10 : a,X11 : a] : (! [X15 : (a > $o)] : (? [X16 : a,X17 : a] : (((((X15 @ (cP @ (cR @ X16) @ (cR @ X17)))) != $true) | (((X15 @ (cP @ (cL @ X16) @ (cL @ X17)))) != $true) | ((cZ != X16) & (cZ = X17))) & (((X15 @ (cP @ X16 @ X17))) = $true)) | (((X15 @ (cP @ (cR @ X10) @ (cR @ X11)))) != $true)) & ? [X12 : (a > $o)] : (! [X13 : a,X14 : a] : (((((X12 @ (cP @ (cR @ X13) @ (cR @ X14)))) = $true) & (((X12 @ (cP @ (cL @ X13) @ (cL @ X14)))) = $true) & ((cZ = X13) | (cZ != X14))) | (((X12 @ (cP @ X13 @ X14))) != $true)) & (((X12 @ (cP @ X10 @ X11))) = $true))) & ! [X0 : (a > $o)] : (! [X3 : a,X4 : a] : ((X3 = X4) | (((X0 @ (cP @ X3 @ X4))) != $true)) | ? [X1 : a,X2 : a] : (((((X0 @ (cP @ (cR @ X1) @ (cR @ X2)))) != $true) | (((X0 @ (cP @ (cL @ X1) @ (cL @ X2)))) != $true) | (((cZ != X2) | (cZ != X1)) & ((cZ = X2) | (cZ = X1)))) & (((X0 @ (cP @ X1 @ X2))) = $true))) & ! [X5 : a] : (((cZ != X5) | (((cP @ (cL @ X5) @ (cR @ X5))) != X5)) & ((((cP @ (cL @ X5) @ (cR @ X5))) = X5) | (cZ = X5))) & ! [X6 : a,X7 : a] : (((cR @ (cP @ X6 @ X7))) = X7) & ! [X8 : a,X9 : a] : (((cL @ (cP @ X8 @ X9))) = X8) & (cZ = ((cR @ cZ))) & (cZ = ((cL @ cZ)))),
% 0.89/0.46 inference(nnf_transformation,[],[f6])).
% 0.89/0.46 thf(f8,plain,(
% 0.89/0.46 ? [X0 : a,X1 : a] : (! [X2 : (a > $o)] : (? [X3 : a,X4 : a] : ((($true != ((X2 @ (cP @ (cR @ X3) @ (cR @ X4))))) | ($true != ((X2 @ (cP @ (cL @ X3) @ (cL @ X4))))) | ((cZ != X3) & (cZ = X4))) & ($true = ((X2 @ (cP @ X3 @ X4))))) | ($true != ((X2 @ (cP @ (cR @ X0) @ (cR @ X1)))))) & ? [X5 : (a > $o)] : (! [X6 : a,X7 : a] : ((($true = ((X5 @ (cP @ (cR @ X6) @ (cR @ X7))))) & ($true = ((X5 @ (cP @ (cL @ X6) @ (cL @ X7))))) & ((cZ = X6) | (cZ != X7))) | ($true != ((X5 @ (cP @ X6 @ X7))))) & ($true = ((X5 @ (cP @ X0 @ X1)))))) & ! [X8 : (a > $o)] : (! [X9 : a,X10 : a] : ((X9 = X10) | ($true != ((X8 @ (cP @ X9 @ X10))))) | ? [X11 : a,X12 : a] : ((($true != ((X8 @ (cP @ (cR @ X11) @ (cR @ X12))))) | ($true != ((X8 @ (cP @ (cL @ X11) @ (cL @ X12))))) | (((cZ != X12) | (cZ != X11)) & ((cZ = X12) | (cZ = X11)))) & ($true = ((X8 @ (cP @ X11 @ X12)))))) & ! [X13 : a] : (((cZ != X13) | (((cP @ (cL @ X13) @ (cR @ X13))) != X13)) & ((((cP @ (cL @ X13) @ (cR @ X13))) = X13) | (cZ = X13))) & ! [X14 : a,X15 : a] : (((cR @ (cP @ X14 @ X15))) = X15) & ! [X16 : a,X17 : a] : (((cL @ (cP @ X16 @ X17))) = X16) & (cZ = ((cR @ cZ))) & (cZ = ((cL @ cZ)))),
% 0.89/0.46 inference(rectify,[],[f7])).
% 0.89/0.46 thf(f9,plain,(
% 0.89/0.46 (! [X2 : (a > $o)] : (((($true != ((X2 @ (cP @ (cR @ (sK2 @ X2)) @ (cR @ (sK3 @ X2)))))) | ($true != ((X2 @ (cP @ (cL @ (sK2 @ X2)) @ (cL @ (sK3 @ X2)))))) | ((cZ != ((sK2 @ X2))) & (cZ = ((sK3 @ X2))))) & ($true = ((X2 @ (cP @ (sK2 @ X2) @ (sK3 @ X2)))))) | ($true != ((X2 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))) & (! [X6 : a,X7 : a] : ((($true = ((sK4 @ (cP @ (cR @ X6) @ (cR @ X7))))) & ($true = ((sK4 @ (cP @ (cL @ X6) @ (cL @ X7))))) & ((cZ = X6) | (cZ != X7))) | ($true != ((sK4 @ (cP @ X6 @ X7))))) & ($true = ((sK4 @ (cP @ sK0 @ sK1)))))) & ! [X8 : (a > $o)] : (! [X9 : a,X10 : a] : ((X9 = X10) | ($true != ((X8 @ (cP @ X9 @ X10))))) | ((($true != ((X8 @ (cP @ (cR @ (sK5 @ X8)) @ (cR @ (sK6 @ X8)))))) | ($true != ((X8 @ (cP @ (cL @ (sK5 @ X8)) @ (cL @ (sK6 @ X8)))))) | (((cZ != ((sK6 @ X8))) | (cZ != ((sK5 @ X8)))) & ((cZ = ((sK6 @ X8))) | (cZ = ((sK5 @ X8)))))) & ($true = ((X8 @ (cP @ (sK5 @ X8) @ (sK6 @ X8))))))) & ! [X13 : a] : (((cZ != X13) | (((cP @ (cL @ X13) @ (cR @ X13))) != X13)) & ((((cP @ (cL @ X13) @ (cR @ X13))) = X13) | (cZ = X13))) & ! [X14 : a,X15 : a] : (((cR @ (cP @ X14 @ X15))) = X15) & ! [X16 : a,X17 : a] : (((cL @ (cP @ X16 @ X17))) = X16) & (cZ = ((cR @ cZ))) & (cZ = ((cL @ cZ)))),
% 0.89/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP,sK4,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X12,sK6 @ X8),skolemize(X12,sK6 @ X8),skolemize(X5,sK4),skolemize(X12,sK6 @ X8),skolemize(X12,sK6 @ X8)],[f8])).
% 0.89/0.46 thf(f19,plain,(
% 0.89/0.46 ($true = ((sK4 @ (cP @ sK0 @ sK1))))),
% 0.89/0.46 inference(cnf_transformation,[],[f9])).
% 0.89/0.46 thf(f20,plain,(
% 0.89/0.46 ( ! [X6 : a,X7 : a] : ((cZ = X6) | (cZ != X7) | ($true != ((sK4 @ (cP @ X6 @ X7))))) )),
% 0.89/0.46 inference(cnf_transformation,[],[f9])).
% 0.89/0.46 thf(f21,plain,(
% 0.89/0.46 ( ! [X6 : a,X7 : a] : (($true != ((sK4 @ (cP @ X6 @ X7)))) | ($true = ((sK4 @ (cP @ (cL @ X6) @ (cL @ X7)))))) )),
% 0.89/0.46 inference(cnf_transformation,[],[f9])).
% 0.89/0.46 thf(f22,plain,(
% 0.89/0.46 ( ! [X6 : a,X7 : a] : (($true != ((sK4 @ (cP @ X6 @ X7)))) | ($true = ((sK4 @ (cP @ (cR @ X6) @ (cR @ X7)))))) )),
% 0.89/0.46 inference(cnf_transformation,[],[f9])).
% 0.89/0.46 thf(f23,plain,(
% 0.89/0.46 ( ! [X2 : (a > $o)] : (($true != ((X2 @ (cP @ (cR @ sK0) @ (cR @ sK1))))) | ($true = ((X2 @ (cP @ (sK2 @ X2) @ (sK3 @ X2)))))) )),
% 0.89/0.46 inference(cnf_transformation,[],[f9])).
% 0.89/0.46 thf(f24,plain,(
% 0.89/0.46 ( ! [X2 : (a > $o)] : (($true != ((X2 @ (cP @ (cL @ (sK2 @ X2)) @ (cL @ (sK3 @ X2)))))) | ($true != ((X2 @ (cP @ (cR @ (sK2 @ X2)) @ (cR @ (sK3 @ X2)))))) | (cZ = ((sK3 @ X2))) | ($true != ((X2 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))) )),
% 0.89/0.46 inference(cnf_transformation,[],[f9])).
% 0.89/0.46 thf(f25,plain,(
% 0.89/0.46 ( ! [X2 : (a > $o)] : (($true != ((X2 @ (cP @ (cL @ (sK2 @ X2)) @ (cL @ (sK3 @ X2)))))) | ($true != ((X2 @ (cP @ (cR @ (sK2 @ X2)) @ (cR @ (sK3 @ X2)))))) | (cZ != ((sK2 @ X2))) | ($true != ((X2 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))) )),
% 0.89/0.46 inference(cnf_transformation,[],[f9])).
% 0.89/0.46 thf(f27,definition,(
% 0.89/0.46 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.89/0.46 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.89/0.46 thf(f28,plain,(
% 0.89/0.46 ( ! [X6 : a] : (($true != ((sK4 @ (cP @ X6 @ cZ)))) | (cZ = X6)) )),
% 0.89/0.46 inference(equality_resolution,[],[f20])).
% 0.89/0.46 thf(f37,plain,(
% 0.89/0.46 ( ! [X0 : a] : (($true != $true) | (cZ = X0) | ($false = ((sK4 @ (cP @ X0 @ cZ))))) )),
% 0.89/0.46 inference(constrained_superposition,[],[f28,f27])).
% 0.89/0.46 thf(f38,plain,(
% 0.89/0.46 ( ! [X0 : a] : (($false = ((sK4 @ (cP @ X0 @ cZ)))) | (cZ = X0)) )),
% 0.89/0.46 inference(trivial_inequality_removal,[],[f37])).
% 0.89/0.46 thf(f60,plain,(
% 0.89/0.46 ($true != $true) | ($true = ((sK4 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.46 inference(constrained_superposition,[],[f22,f19])).
% 0.89/0.46 thf(f70,plain,(
% 0.89/0.46 ($true = ((sK4 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.46 inference(trivial_inequality_removal,[],[f60])).
% 0.89/0.46 thf(f348,plain,(
% 0.89/0.46 ($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (sK2 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK3 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))))),
% 0.89/0.46 inference(constrained_superposition,[],[f23,f70])).
% 0.89/0.46 thf(f382,plain,(
% 0.89/0.46 ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (sK2 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK3 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))))),
% 0.89/0.46 inference(trivial_inequality_removal,[],[f348])).
% 0.89/0.46 thf(f383,plain,(
% 0.89/0.46 ($true = ((sK4 @ (cP @ (sK2 @ sK4) @ (sK3 @ sK4)))))),
% 0.89/0.46 inference(beta-eta_normalization,[],[f382])).
% 0.89/0.46 thf(f410,plain,(
% 0.89/0.46 ($true != $true) | ($true = ((sK4 @ (cP @ (cR @ (sK2 @ sK4)) @ (cR @ (sK3 @ sK4))))))),
% 0.89/0.46 inference(constrained_superposition,[],[f22,f383])).
% 0.89/0.46 thf(f411,plain,(
% 0.89/0.46 ($true != $true) | ($true = ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4))))))),
% 0.89/0.46 inference(constrained_superposition,[],[f21,f383])).
% 0.89/0.46 thf(f421,plain,(
% 0.89/0.46 ($true = ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4))))))),
% 0.89/0.46 inference(trivial_inequality_removal,[],[f411])).
% 0.89/0.46 thf(f422,plain,(
% 0.89/0.46 ($true = ((sK4 @ (cP @ (cR @ (sK2 @ sK4)) @ (cR @ (sK3 @ sK4))))))),
% 0.89/0.46 inference(trivial_inequality_removal,[],[f410])).
% 0.89/0.46 thf(f1597,plain,(
% 0.89/0.46 ($true != $true) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (cR @ (sK2 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))) @ (cR @ (sK3 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))))) | (cZ = ((sK3 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.46 inference(constrained_superposition,[],[f24,f421])).
% 0.89/0.46 thf(f1662,plain,(
% 0.89/0.46 ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (cR @ (sK2 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))) @ (cR @ (sK3 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))))) | (cZ = ((sK3 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.46 inference(trivial_inequality_removal,[],[f1597])).
% 0.89/0.46 thf(f1663,plain,(
% 0.89/0.46 ($true != ((sK4 @ (cP @ (cR @ (sK2 @ sK4)) @ (cR @ (sK3 @ sK4)))))) | (cZ = ((sK3 @ sK4))) | ($true != ((sK4 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.46 inference(beta-eta_normalization,[],[f1662])).
% 0.89/0.46 thf(f1710,plain,(
% 0.89/0.46 (cZ = ((sK3 @ sK4))) | ($true != ((sK4 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.46 inference(forward_subsumption_resolution,[],[f1663,f422])).
% 0.89/0.46 thf(f1720,plain,(
% 0.89/0.46 (cZ = ((sK3 @ sK4)))),
% 0.89/0.46 inference(forward_subsumption_resolution,[],[f1710,f70])).
% 0.89/0.46 thf(f1823,plain,(
% 0.89/0.46 ($true = ((sK4 @ (cP @ (sK2 @ sK4) @ cZ))))),
% 0.89/0.46 inference(constrained_superposition,[],[f383,f1720])).
% 0.89/0.46 thf(f1871,plain,(
% 0.89/0.46 ($true = $false) | (cZ = ((sK2 @ sK4)))),
% 0.89/0.46 inference(constrained_superposition,[],[f38,f1823])).
% 0.89/0.46 thf(f1888,plain,(
% 0.89/0.46 (cZ = ((sK2 @ sK4)))),
% 0.89/0.46 inference(trivial_inequality_removal,[],[f1871])).
% 0.89/0.47 thf(f2061,plain,(
% 0.89/0.47 ($true != $true) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (cR @ (sK2 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))) @ (cR @ (sK3 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))))) | (cZ != ((sK2 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.47 inference(constrained_superposition,[],[f25,f421])).
% 0.89/0.47 thf(f2114,plain,(
% 0.89/0.47 ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (cR @ (sK2 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))) @ (cR @ (sK3 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))))) | (cZ != ((sK2 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.47 inference(trivial_inequality_removal,[],[f2061])).
% 0.89/0.47 thf(f2115,plain,(
% 0.89/0.47 ($true != ((sK4 @ (cP @ (cR @ (sK2 @ sK4)) @ (cR @ (sK3 @ sK4)))))) | (cZ != ((sK2 @ sK4))) | ($true != ((sK4 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.47 inference(beta-eta_normalization,[],[f2114])).
% 0.89/0.47 thf(f2158,plain,(
% 0.89/0.47 (cZ != ((sK2 @ sK4))) | ($true != ((sK4 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.47 inference(forward_subsumption_resolution,[],[f2115,f422])).
% 0.89/0.47 thf(f2169,plain,(
% 0.89/0.47 ($true != ((sK4 @ (cP @ (cR @ sK0) @ (cR @ sK1)))))),
% 0.89/0.47 inference(forward_subsumption_resolution,[],[f2158,f1888])).
% 0.89/0.47 thf(f2174,plain,(
% 0.89/0.47 $false),
% 0.89/0.47 inference(forward_subsumption_resolution,[],[f2169,f70])).
% 0.89/0.47 % SZS output end Proof for theBenchmark
% 0.89/0.47 % (1769222)------------------------------
% 0.89/0.47 % (1769222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.47 % (1769222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.47 % (1769222)CaDiCaL version: 2.1.3
% 0.89/0.47 % (1769222)Termination reason: Refutation
% 0.89/0.47 % (1769222)Time elapsed: 0.122 s
% 0.89/0.47 % (1769222)Peak memory usage: 13 MB
% 0.89/0.47 % (1769222)Instructions burned: 263 (million)
% 0.89/0.47 % (1769189)Success in time 0.235 s
% 0.89/0.47 % Vampire exiting
%------------------------------------------------------------------------------