%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX206-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 01:46:10 PM UTC 2026
% Result : Unsatisfiable 2.58s 1.12s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 50 ( 50 unt; 9 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : impl(btrue,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
fof(f4,negated_conjecture,
! [X0] : x2(z,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
fof(f6,negated_conjecture,
! [X0] : plus_not_idem(X0) = impl(eq(x2(X0,X0),X0),eq2(btrue,bfalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(f9,axiom,
eq2(btrue,bfalse) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(f10,plain,
bfalse = eq2(btrue,bfalse),
inference(reorient_equations,[],[f9]) ).
fof(f16,axiom,
! [X0] : eq(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f17,plain,
! [X0] : btrue = eq(X0,X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f19,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
! [X0] : eq2(plus_not_idem(X0),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f21,plain,
! [X0] : btrue != eq2(plus_not_idem(X0),bfalse),
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
! [X0] : btrue != eq2(impl(eq(x2(X0,X0),X0),eq2(btrue,bfalse)),bfalse),
inference(definition_unfolding,[],[f21,f6]) ).
fof(f23,definition,
! [X0] : sF0(X0) = impl(btrue,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f24,plain,
! [X0] : impl(btrue,X0) = sF0(X0),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f24]) ).
fof(f29,definition,
! [X0] : sF2(X0) = x2(z,X0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f30,plain,
! [X0] : x2(z,X0) = sF2(X0),
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
! [X0] : sF2(X0) = X0,
inference(definition_folding,[],[f4,f30]) ).
fof(f40,definition,
sF6 = eq2(btrue,bfalse),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f41,plain,
eq2(btrue,bfalse) = sF6,
inference(reorient_equations,[],[f40]) ).
fof(f42,plain,
bfalse = sF6,
inference(definition_folding,[],[f10,f41]) ).
fof(f52,definition,
! [X0] : sF10(X0) = eq(X0,X0),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f53,plain,
! [X0] : eq(X0,X0) = sF10(X0),
inference(reorient_equations,[],[f52]) ).
fof(f54,plain,
! [X0] : btrue = sF10(X0),
inference(definition_folding,[],[f17,f53]) ).
fof(f55,definition,
! [X0] : sF11(X0) = eq2(X0,X0),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f56,plain,
! [X0] : eq2(X0,X0) = sF11(X0),
inference(reorient_equations,[],[f55]) ).
fof(f57,plain,
! [X0] : btrue = sF11(X0),
inference(definition_folding,[],[f19,f56]) ).
fof(f58,definition,
! [X0] : sF12(X0) = x2(X0,X0),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f59,plain,
! [X0] : x2(X0,X0) = sF12(X0),
inference(reorient_equations,[],[f58]) ).
fof(f60,definition,
! [X0] : sF13(X0) = eq(sF12(X0),X0),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f61,plain,
! [X0] : eq(sF12(X0),X0) = sF13(X0),
inference(reorient_equations,[],[f60]) ).
fof(f62,definition,
! [X0] : sF14(X0) = impl(sF13(X0),sF6),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f63,plain,
! [X0] : impl(sF13(X0),sF6) = 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,f41,f61,f59]) ).
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,[],[f57,f56]) ).
fof(f69,plain,
! [X0] : btrue = eq(X0,X0),
inference(forward_demodulation,[],[f54,f53]) ).
fof(f74,plain,
! [X0] : x2(z,X0) = X0,
inference(forward_demodulation,[],[f31,f30]) ).
fof(f76,plain,
! [X0] : impl(btrue,X0) = X0,
inference(forward_demodulation,[],[f25,f24]) ).
fof(f77,plain,
! [X0] : btrue != eq2(impl(sF13(X0),sF6),bfalse),
inference(forward_demodulation,[],[f67,f63]) ).
fof(f79,plain,
! [X0] : btrue != eq2(impl(eq(sF12(X0),X0),sF6),bfalse),
inference(forward_demodulation,[],[f77,f61]) ).
fof(f80,plain,
! [X0] : btrue != eq2(impl(eq(x2(X0,X0),X0),sF6),bfalse),
inference(forward_demodulation,[],[f79,f59]) ).
fof(f83,plain,
! [X0] : btrue != eq2(impl(eq(x2(X0,X0),X0),bfalse),bfalse),
inference(forward_demodulation,[],[f80,f42]) ).
fof(f84,plain,
btrue != eq2(impl(eq(z,z),bfalse),bfalse),
inference(superposition,[],[f83,f74]) ).
fof(f87,plain,
btrue != eq2(impl(btrue,bfalse),bfalse),
inference(forward_demodulation,[],[f84,f69]) ).
fof(f88,plain,
btrue != eq2(bfalse,bfalse),
inference(forward_demodulation,[],[f87,f76]) ).
fof(f89,plain,
btrue != btrue,
inference(forward_demodulation,[],[f88,f68]) ).
fof(f90,plain,
$false,
inference(trivial_inequality_removal,[],[f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX206-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 15:09:51 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.58/1.12 % (449033)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.58/1.12 % (449107)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4134908403:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.58/1.12 % (449107)First to succeed.
% 2.58/1.12 % (449107)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-449033"
% 2.58/1.12 % (449106)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1400666464:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.58/1.12 % (449109)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1673027683:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.58/1.12 % (449103)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=312094474:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.58/1.12 % (449108)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3296474077:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.58/1.12 % (449105)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1844206439:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.58/1.12 % (449104)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=960326958:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.58/1.12 % (449106)Also succeeded, but the first one will report.
% 2.58/1.12 % (449109)Also succeeded, but the first one will report.
% 2.58/1.12 % (449107)Refutation found. Thanks to Tanya!
% 2.58/1.12 % SZS status Unsatisfiable for theBenchmark
% 2.58/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.12 % (449107)------------------------------
% 2.58/1.12 % (449107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.12 % (449107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.12 % (449107)CaDiCaL version: 2.1.3
% 2.58/1.12 % (449107)Termination reason: Refutation
% 2.58/1.12 % (449107)Time elapsed: 0.002 s
% 2.58/1.12 % (449107)Peak memory usage: 88 MB
% 2.58/1.12 % (449107)Instructions burned: 3 (million)
% 2.58/1.12 % (449107)------------------------------
% 2.58/1.12 % (449107)------------------------------
% 2.58/1.12 % (449033)Success in time 0.279 s
% 2.58/1.12 % Vampire exiting
%------------------------------------------------------------------------------