%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:46:09 PM UTC 2026
% Result : Unsatisfiable 2.45s 1.11s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 64 ( 64 unt; 11 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 18 ( 18 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : x2(z,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : x2(s(X0),X1) = s(x2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(f5,negated_conjecture,
! [X0,X1] : x22(s(X0),X1) = x2(X1,x22(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(f6,negated_conjecture,
! [X0] : mul_idem(X0) = eq(x22(X0,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
fof(f11,negated_conjecture,
! [X0,X1] : eq(s(X0),s(X1)) = eq(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f14,axiom,
! [X0] : eq(s(X0),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(f15,plain,
! [X0] : bfalse = eq(s(X0),z),
inference(reorient_equations,[],[f14]) ).
fof(f18,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
fof(f19,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
! [X0] : eq2(mul_idem(X0),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f21,plain,
! [X0] : btrue != eq2(mul_idem(X0),bfalse),
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
! [X0] : btrue != eq2(eq(x22(X0,X0),X0),bfalse),
inference(definition_unfolding,[],[f21,f6]) ).
fof(f23,definition,
! [X0] : sF0(X0) = x2(z,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f24,plain,
! [X0] : x2(z,X0) = sF0(X0),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f24]) ).
fof(f26,definition,
! [X0,X1] : sF1(X0,X1) = x2(s(X0),X1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f27,plain,
! [X0,X1] : x2(s(X0),X1) = sF1(X0,X1),
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
! [X0,X1] : sF2(X0,X1) = s(x2(X0,X1)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f29,plain,
! [X0,X1] : s(x2(X0,X1)) = sF2(X0,X1),
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
! [X0,X1] : sF1(X0,X1) = sF2(X0,X1),
inference(definition_folding,[],[f2,f29,f27]) ).
fof(f34,definition,
! [X0,X1] : sF4(X0,X1) = x22(s(X0),X1),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f35,plain,
! [X0,X1] : x22(s(X0),X1) = sF4(X0,X1),
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
! [X0,X1] : sF5(X1,X0) = x2(X1,x22(X0,X1)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f37,plain,
! [X0,X1] : x2(X1,x22(X0,X1)) = sF5(X1,X0),
inference(reorient_equations,[],[f36]) ).
fof(f38,plain,
! [X0,X1] : sF4(X0,X1) = sF5(X1,X0),
inference(definition_folding,[],[f5,f37,f35]) ).
fof(f45,definition,
! [X0,X1] : sF8(X0,X1) = eq(s(X0),s(X1)),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f46,plain,
! [X0,X1] : eq(s(X0),s(X1)) = sF8(X0,X1),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X0,X1] : eq(X0,X1) = sF8(X0,X1),
inference(definition_folding,[],[f11,f46]) ).
fof(f51,definition,
! [X0] : sF10(X0) = eq(s(X0),z),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f52,plain,
! [X0] : eq(s(X0),z) = sF10(X0),
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
! [X0] : bfalse = sF10(X0),
inference(definition_folding,[],[f15,f52]) ).
fof(f57,definition,
! [X0] : sF12(X0) = eq2(X0,X0),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f58,plain,
! [X0] : eq2(X0,X0) = sF12(X0),
inference(reorient_equations,[],[f57]) ).
fof(f59,plain,
! [X0] : btrue = sF12(X0),
inference(definition_folding,[],[f19,f58]) ).
fof(f60,definition,
! [X0] : sF13(X0) = x22(X0,X0),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f61,plain,
! [X0] : x22(X0,X0) = sF13(X0),
inference(reorient_equations,[],[f60]) ).
fof(f62,definition,
! [X0] : sF14(X0) = eq(sF13(X0),X0),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f63,plain,
! [X0] : eq(sF13(X0),X0) = sF14(X0),
inference(reorient_equations,[],[f62]) ).
fof(f64,definition,
! [X0] : sF15(X0) = eq2(sF14(X0),bfalse),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f65,plain,
! [X0] : eq2(sF14(X0),bfalse) = sF15(X0),
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
! [X0] : btrue != sF15(X0),
inference(definition_folding,[],[f22,f65,f63,f61]) ).
fof(f67,plain,
! [X0] : btrue != eq2(sF14(X0),bfalse),
inference(forward_demodulation,[],[f66,f65]) ).
fof(f68,plain,
! [X0] : btrue = eq2(X0,X0),
inference(forward_demodulation,[],[f59,f58]) ).
fof(f70,plain,
! [X0] : bfalse = eq(s(X0),z),
inference(forward_demodulation,[],[f53,f52]) ).
fof(f72,plain,
! [X0,X1] : eq(s(X0),s(X1)) = eq(X0,X1),
inference(forward_demodulation,[],[f47,f46]) ).
fof(f73,plain,
! [X0,X1] : x2(X1,x22(X0,X1)) = sF4(X0,X1),
inference(forward_demodulation,[],[f38,f37]) ).
fof(f75,plain,
! [X0,X1] : s(x2(X0,X1)) = sF1(X0,X1),
inference(forward_demodulation,[],[f30,f29]) ).
fof(f76,plain,
! [X0] : x2(z,X0) = X0,
inference(forward_demodulation,[],[f25,f24]) ).
fof(f77,plain,
! [X0] : btrue != eq2(eq(sF13(X0),X0),bfalse),
inference(forward_demodulation,[],[f67,f63]) ).
fof(f78,plain,
! [X0,X1] : x22(s(X0),X1) = x2(X1,x22(X0,X1)),
inference(forward_demodulation,[],[f73,f35]) ).
fof(f79,plain,
! [X0,X1] : x2(s(X0),X1) = s(x2(X0,X1)),
inference(forward_demodulation,[],[f75,f27]) ).
fof(f80,plain,
! [X0] : btrue != eq2(eq(x22(X0,X0),X0),bfalse),
inference(forward_demodulation,[],[f77,f61]) ).
fof(f87,plain,
! [X0] : btrue != eq2(eq(x2(s(X0),x22(X0,s(X0))),s(X0)),bfalse),
inference(superposition,[],[f80,f78]) ).
fof(f88,plain,
! [X0] : btrue != eq2(eq(s(x2(X0,x22(X0,s(X0)))),s(X0)),bfalse),
inference(forward_demodulation,[],[f87,f79]) ).
fof(f89,plain,
! [X0] : btrue != eq2(eq(x2(X0,x22(X0,s(X0))),X0),bfalse),
inference(forward_demodulation,[],[f88,f72]) ).
fof(f93,plain,
! [X0] : btrue != eq2(eq(s(x2(X0,x22(s(X0),s(s(X0))))),s(X0)),bfalse),
inference(superposition,[],[f89,f79]) ).
fof(f94,plain,
! [X0] : btrue != eq2(eq(x2(X0,x22(s(X0),s(s(X0)))),X0),bfalse),
inference(forward_demodulation,[],[f93,f72]) ).
fof(f98,plain,
! [X0] : btrue != eq2(eq(x2(X0,x2(s(s(X0)),x22(X0,s(s(X0))))),X0),bfalse),
inference(forward_demodulation,[],[f94,f78]) ).
fof(f102,plain,
! [X0] : btrue != eq2(eq(x2(X0,s(x2(s(X0),x22(X0,s(s(X0)))))),X0),bfalse),
inference(forward_demodulation,[],[f98,f79]) ).
fof(f106,plain,
! [X0] : btrue != eq2(eq(x2(X0,s(s(x2(X0,x22(X0,s(s(X0))))))),X0),bfalse),
inference(forward_demodulation,[],[f102,f79]) ).
fof(f114,plain,
btrue != eq2(eq(s(s(x2(z,x22(z,s(s(z)))))),z),bfalse),
inference(superposition,[],[f106,f76]) ).
fof(f117,plain,
btrue != eq2(bfalse,bfalse),
inference(forward_demodulation,[],[f114,f70]) ).
fof(f123,plain,
btrue != btrue,
inference(forward_demodulation,[],[f117,f68]) ).
fof(f124,plain,
$false,
inference(trivial_inequality_removal,[],[f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n015.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Mon Sep 28 15:13:15 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 2.45/1.11 % (2705872)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.45/1.11 % (2705944)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2215122478:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.45/1.11 % (2705944)First to succeed.
% 2.45/1.11 % (2705944)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2705872"
% 2.45/1.11 % (2705946)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3557832073:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.45/1.11 % (2705942)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3707569087:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.45/1.11 % (2705943)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4031790987:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.45/1.11 % (2705941)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=1309098158:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.45/1.11 % (2705940)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=2715432364:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.45/1.11 % (2705946)Also succeeded, but the first one will report.
% 2.45/1.11 % (2705945)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4214379689:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.45/1.11 % (2705943)Also succeeded, but the first one will report.
% 2.45/1.11 % (2705944)Refutation found. Thanks to Tanya!
% 2.45/1.11 % SZS status Unsatisfiable for theBenchmark
% 2.45/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 2.45/1.11 % (2705944)------------------------------
% 2.45/1.11 % (2705944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.11 % (2705944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.11 % (2705944)CaDiCaL version: 2.1.3
% 2.45/1.11 % (2705944)Termination reason: Refutation
% 2.45/1.11 % (2705944)Time elapsed: 0.002 s
% 2.45/1.11 % (2705944)Peak memory usage: 88 MB
% 2.45/1.11 % (2705944)Instructions burned: 5 (million)
% 2.45/1.11 % (2705944)------------------------------
% 2.45/1.11 % (2705944)------------------------------
% 2.45/1.11 % (2705872)Success in time 0.259 s
% 2.45/1.11 % Vampire exiting
%------------------------------------------------------------------------------