%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN563-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Tue Sep 29 02:00:58 PM UTC 2026
% Result : Unsatisfiable 6.25s 1.56s
% Output : Refutation 6.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of formulae : 75 ( 75 unt; 6 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-4 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,negated_conjecture,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,negated_conjecture,
! [X0] : p2(X0,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
fof(f4,negated_conjecture,
! [X0] : p6(X0,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_2) ).
fof(f5,plain,
! [X0] : true = p6(X0,X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
p2(f4(c7),f4(c8)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_4) ).
fof(f7,plain,
true = p2(f4(c7),f4(c8)),
inference(reorient_equations,[],[f6]) ).
fof(f10,negated_conjecture,
! [X0] : p5(f3(f3(X0)),f3(f4(X0))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_7) ).
fof(f11,plain,
! [X0] : true = p5(f3(f3(X0)),f3(f4(X0))),
inference(reorient_equations,[],[f10]) ).
fof(f14,negated_conjecture,
! [X0] : ifeq2(p6(c7,X0),true,p6(c7,f3(X0)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_9) ).
fof(f15,plain,
! [X0] : true = ifeq2(p6(c7,X0),true,p6(c7,f3(X0)),true),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
! [X0,X1] : ifeq2(p5(X0,X1),true,p6(f4(X0),X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_10) ).
fof(f17,plain,
! [X0,X1] : true = ifeq2(p5(X0,X1),true,p6(f4(X0),X1),true),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
! [X0,X1] : ifeq2(p2(X0,X1),true,p2(f3(X0),f3(X1)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
fof(f19,plain,
! [X0,X1] : true = ifeq2(p2(X0,X1),true,p2(f3(X0),f3(X1)),true),
inference(reorient_equations,[],[f18]) ).
fof(f22,negated_conjecture,
! [X2,X0,X1] : ifeq2(p2(X0,X1),true,ifeq2(p2(X0,X2),true,p2(X2,X1),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_13) ).
fof(f23,plain,
! [X2,X0,X1] : true = ifeq2(p2(X0,X1),true,ifeq2(p2(X0,X2),true,p2(X2,X1),true),true),
inference(reorient_equations,[],[f22]) ).
fof(f26,negated_conjecture,
! [X2,X0,X1] : ifeq2(p6(X0,X1),true,ifeq2(p5(X1,X2),true,p5(X0,X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_15) ).
fof(f27,plain,
! [X2,X0,X1] : true = ifeq2(p6(X0,X1),true,ifeq2(p5(X1,X2),true,p5(X0,X2),true),true),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
! [X2,X3,X0,X1] : ifeq2(p2(X0,X1),true,ifeq2(p2(X2,X3),true,ifeq2(p6(X2,X0),true,p6(X3,X1),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_16) ).
fof(f29,plain,
! [X2,X3,X0,X1] : true = ifeq2(p2(X0,X1),true,ifeq2(p2(X2,X3),true,ifeq2(p6(X2,X0),true,p6(X3,X1),true),true),true),
inference(reorient_equations,[],[f28]) ).
fof(f34,negated_conjecture,
ifeq(p6(f4(c7),f3(f4(c8))),true,a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p6_5) ).
fof(f35,plain,
b = ifeq(p6(f4(c7),f3(f4(c8))),true,a,b),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f37,definition,
sF0 = f4(c7),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f38,plain,
f4(c7) = sF0,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF1 = f4(c8),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f40,plain,
f4(c8) = sF1,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF2 = p2(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f42,plain,
p2(sF0,sF1) = sF2,
inference(reorient_equations,[],[f41]) ).
fof(f43,plain,
true = sF2,
inference(definition_folding,[],[f7,f42,f40,f38]) ).
fof(f49,definition,
sF5 = f3(sF1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f50,plain,
f3(sF1) = sF5,
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
sF6 = p6(sF0,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f52,plain,
p6(sF0,sF5) = sF6,
inference(reorient_equations,[],[f51]) ).
fof(f53,definition,
sF7 = ifeq(sF6,true,a,b),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f54,plain,
ifeq(sF6,true,a,b) = sF7,
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
b = sF7,
inference(definition_folding,[],[f35,f54,f52,f50,f40,f38]) ).
fof(f56,plain,
true = p2(sF0,sF1),
inference(forward_demodulation,[],[f42,f43]) ).
fof(f58,plain,
b = ifeq(sF6,true,a,b),
inference(forward_demodulation,[],[f54,f55]) ).
fof(f60,plain,
! [X0,X1] : true = ifeq2(p2(X0,X1),true,ifeq2(true,true,ifeq2(p6(sF0,X0),true,p6(sF1,X1),true),true),true),
inference(superposition,[],[f29,f56]) ).
fof(f66,plain,
! [X0,X1] : true = ifeq2(p2(X0,sF5),true,ifeq2(p2(X1,sF0),true,ifeq2(p6(X1,X0),true,sF6,true),true),true),
inference(superposition,[],[f29,f52]) ).
fof(f68,plain,
! [X0,X1] : true = ifeq2(p2(X0,X1),true,ifeq2(p6(sF0,X0),true,p6(sF1,X1),true),true),
inference(forward_demodulation,[],[f60,f1]) ).
fof(f100,plain,
! [X0,X1] : true = ifeq2(p6(X0,f3(f3(X1))),true,ifeq2(true,true,p5(X0,f3(f4(X1))),true),true),
inference(superposition,[],[f27,f11]) ).
fof(f102,plain,
! [X0,X1] : true = ifeq2(p6(X0,f3(f3(X1))),true,p5(X0,f3(f4(X1))),true),
inference(forward_demodulation,[],[f100,f1]) ).
fof(f104,plain,
! [X0,X1] : true = ifeq2(true,true,ifeq2(p2(X0,X1),true,p2(X1,X0),true),true),
inference(superposition,[],[f23,f3]) ).
fof(f116,plain,
! [X0,X1] : true = ifeq2(p2(X0,X1),true,p2(X1,X0),true),
inference(forward_demodulation,[],[f104,f1]) ).
fof(f117,plain,
true = ifeq2(true,true,p6(c7,f3(c7)),true),
inference(superposition,[],[f15,f5]) ).
fof(f122,plain,
true = p6(c7,f3(c7)),
inference(forward_demodulation,[],[f117,f1]) ).
fof(f187,plain,
true = ifeq2(true,true,p2(f3(sF0),f3(sF1)),true),
inference(superposition,[],[f19,f56]) ).
fof(f195,plain,
true = p2(f3(sF0),f3(sF1)),
inference(forward_demodulation,[],[f187,f1]) ).
fof(f196,plain,
true = p2(f3(sF0),sF5),
inference(forward_demodulation,[],[f195,f50]) ).
fof(f266,plain,
true = ifeq2(true,true,p6(c7,f3(f3(c7))),true),
inference(superposition,[],[f15,f122]) ).
fof(f285,plain,
true = p6(c7,f3(f3(c7))),
inference(forward_demodulation,[],[f266,f1]) ).
fof(f310,plain,
true = ifeq2(true,true,p2(sF1,sF0),true),
inference(superposition,[],[f116,f56]) ).
fof(f319,plain,
true = p2(sF1,sF0),
inference(forward_demodulation,[],[f310,f1]) ).
fof(f636,plain,
true = ifeq2(true,true,p5(c7,f3(f4(c7))),true),
inference(superposition,[],[f102,f285]) ).
fof(f646,plain,
true = p5(c7,f3(f4(c7))),
inference(forward_demodulation,[],[f636,f1]) ).
fof(f648,plain,
true = p5(c7,f3(sF0)),
inference(forward_demodulation,[],[f646,f38]) ).
fof(f652,plain,
true = ifeq2(true,true,p6(f4(c7),f3(sF0)),true),
inference(superposition,[],[f17,f648]) ).
fof(f666,plain,
true = p6(f4(c7),f3(sF0)),
inference(forward_demodulation,[],[f652,f1]) ).
fof(f669,plain,
true = p6(sF0,f3(sF0)),
inference(forward_demodulation,[],[f666,f38]) ).
fof(f1289,plain,
true = ifeq2(true,true,ifeq2(p6(sF0,f3(sF0)),true,p6(sF1,sF5),true),true),
inference(superposition,[],[f68,f196]) ).
fof(f1320,plain,
true = ifeq2(p6(sF0,f3(sF0)),true,p6(sF1,sF5),true),
inference(forward_demodulation,[],[f1289,f1]) ).
fof(f1326,plain,
true = ifeq2(true,true,p6(sF1,sF5),true),
inference(forward_demodulation,[],[f1320,f669]) ).
fof(f1331,plain,
true = p6(sF1,sF5),
inference(forward_demodulation,[],[f1326,f1]) ).
fof(f1451,plain,
true = ifeq2(p2(sF5,sF5),true,ifeq2(p2(sF1,sF0),true,ifeq2(true,true,sF6,true),true),true),
inference(superposition,[],[f66,f1331]) ).
fof(f1452,plain,
true = ifeq2(p2(sF5,sF5),true,ifeq2(p2(sF1,sF0),true,sF6,true),true),
inference(forward_demodulation,[],[f1451,f1]) ).
fof(f1484,plain,
true = ifeq2(p2(sF5,sF5),true,ifeq2(true,true,sF6,true),true),
inference(forward_demodulation,[],[f1452,f319]) ).
fof(f1495,plain,
true = ifeq2(p2(sF5,sF5),true,sF6,true),
inference(forward_demodulation,[],[f1484,f1]) ).
fof(f1505,plain,
true = ifeq2(true,true,sF6,true),
inference(forward_demodulation,[],[f1495,f3]) ).
fof(f1520,plain,
true = sF6,
inference(forward_demodulation,[],[f1505,f1]) ).
fof(f1540,plain,
b = ifeq(sF6,sF6,a,b),
inference(backward_demodulation,[],[f58,f1520]) ).
fof(f2182,plain,
a = b,
inference(forward_demodulation,[],[f1540,f2]) ).
fof(f2183,plain,
$false,
inference(forward_subsumption_resolution,[],[f2182,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN563-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n008.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 16:30:09 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.55/1.47 % (2382771)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.55/1.47 % (2382778)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3899322943:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.55/1.47 % (2382776)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2418653001:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.55/1.47 % (2382777)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3526370703:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.55/1.47 % (2382780)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=245145896:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.55/1.47 % (2382782)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2140604570:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.55/1.47 % (2382779)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=282483800:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.55/1.47 % (2382781)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=576806498:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.55/1.47 % (2382779)Instruction limit reached!
% 5.55/1.47 % (2382779)------------------------------
% 5.55/1.47 % (2382779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.47 % (2382779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.47 % (2382779)CaDiCaL version: 2.1.3
% 5.55/1.47 % (2382779)Termination reason: Instruction limit
% 5.55/1.47 % (2382779)Termination phase: Saturation
% 5.55/1.47 % (2382779)Time elapsed: 0.077 s
% 5.55/1.47 % (2382779)Peak memory usage: 88 MB
% 5.55/1.47 % (2382779)Instructions burned: 137 (million)
% 5.55/1.47 % (2382780)Instruction limit reached!
% 5.55/1.47 % (2382780)------------------------------
% 5.55/1.47 % (2382780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.47 % (2382780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.47 % (2382780)CaDiCaL version: 2.1.3
% 5.55/1.47 % (2382780)Termination reason: Instruction limit
% 5.55/1.47 % (2382780)Termination phase: Saturation
% 5.55/1.47 % (2382780)Time elapsed: 0.098 s
% 5.55/1.47 % (2382780)Peak memory usage: 89 MB
% 5.55/1.47 % (2382780)Instructions burned: 182 (million)
% 5.55/1.47 % (2382781)Instruction limit reached!
% 5.55/1.47 % (2382781)------------------------------
% 5.55/1.47 % (2382781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.47 % (2382781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.47 % (2382781)CaDiCaL version: 2.1.3
% 5.55/1.47 % (2382781)Termination reason: Instruction limit
% 5.55/1.47 % (2382781)Termination phase: Saturation
% 5.55/1.47 % (2382781)Time elapsed: 0.150 s
% 5.55/1.47 % (2382781)Peak memory usage: 90 MB
% 5.55/1.47 % (2382781)Instructions burned: 257 (million)
% 5.55/1.47 % (2382790)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2609754463:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.55/1.47 % (2382791)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3271422225:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.55/1.47 % (2382792)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=87554904:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.55/1.47 % (2382792)Instruction limit reached!
% 5.55/1.47 % (2382792)------------------------------
% 5.55/1.47 % (2382792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.47 % (2382792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.47 % (2382792)CaDiCaL version: 2.1.3
% 5.55/1.47 % (2382792)Termination reason: Instruction limit
% 5.55/1.47 % (2382792)Termination phase: Saturation
% 5.55/1.47 % (2382792)Time elapsed: 0.103 s
% 6.25/1.56 % (2382792)Peak memory usage: 91 MB
% 6.25/1.56 % (2382792)Instructions burned: 215 (million)
% 6.25/1.56 % (2382778)First to succeed.
% 6.25/1.56 % (2382778)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2382771"
% 6.25/1.56 % (2382782)Also succeeded, but the first one will report.
% 6.25/1.56 % (2382796)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=2046857339:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 6.25/1.56 % (2382778)Refutation found. Thanks to Tanya!
% 6.25/1.56 % SZS status Unsatisfiable for theBenchmark
% 6.25/1.56 % SZS output start Proof for theBenchmark
% See solution above
% 6.25/1.57 % (2382778)------------------------------
% 6.25/1.57 % (2382778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.57 % (2382778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.57 % (2382778)CaDiCaL version: 2.1.3
% 6.25/1.57 % (2382778)Termination reason: Refutation
% 6.25/1.57 % (2382778)Time elapsed: 0.529 s
% 6.25/1.57 % (2382778)Peak memory usage: 132 MB
% 6.25/1.57 % (2382778)Instructions burned: 1399 (million)
% 6.25/1.57 % (2382778)------------------------------
% 6.25/1.57 % (2382778)------------------------------
% 6.25/1.57 % (2382771)Success in time 0.813 s
% 6.25/1.57 % Vampire exiting
%------------------------------------------------------------------------------