%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ROB002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:36:14 PM UTC 2026
% Result : Unsatisfiable 3.04s 1.10s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 55 ( 55 unt; 13 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f3,negated_conjecture,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',robbins_axiom) ).
fof(f4,negated_conjecture,
! [X0] : negate(negate(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',double_negation) ).
fof(f5,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
fof(f6,plain,
b != add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),
inference(reorient_equations,[],[f5]) ).
fof(f12,definition,
! [X0,X1] : sF2(X0,X1) = negate(add(X0,X1)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f13,plain,
! [X0,X1] : negate(add(X0,X1)) = sF2(X0,X1),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X0,X1] : sF3(X0,X1) = add(X0,negate(X1)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
! [X0,X1] : add(X0,negate(X1)) = sF3(X0,X1),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
! [X0,X1] : sF4(X0,X1) = negate(sF3(X0,X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f17,plain,
! [X0,X1] : negate(sF3(X0,X1)) = sF4(X0,X1),
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
! [X0,X1] : sF5(X0,X1) = add(sF2(X0,X1),sF4(X0,X1)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f19,plain,
! [X0,X1] : add(sF2(X0,X1),sF4(X0,X1)) = sF5(X0,X1),
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
! [X0,X1] : sF6(X0,X1) = negate(sF5(X0,X1)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f21,plain,
! [X0,X1] : negate(sF5(X0,X1)) = sF6(X0,X1),
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
! [X0,X1] : sF6(X0,X1) = X0,
inference(definition_folding,[],[f3,f21,f19,f17,f15,f13]) ).
fof(f23,definition,
! [X0] : sF7(X0) = negate(negate(X0)),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f24,plain,
! [X0] : negate(negate(X0)) = sF7(X0),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : sF7(X0) = X0,
inference(definition_folding,[],[f4,f24]) ).
fof(f26,definition,
sF8 = negate(b),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f27,plain,
negate(b) = sF8,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF9 = add(a,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f29,plain,
add(a,sF8) = sF9,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF10 = negate(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f31,plain,
negate(sF9) = sF10,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF11 = negate(a),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f33,plain,
negate(a) = sF11,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF12 = add(sF11,sF8),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f35,plain,
add(sF11,sF8) = sF12,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF13 = negate(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f37,plain,
negate(sF12) = sF13,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF14 = add(sF10,sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f39,plain,
add(sF10,sF13) = sF14,
inference(reorient_equations,[],[f38]) ).
fof(f40,plain,
b != sF14,
inference(definition_folding,[],[f6,f39,f37,f35,f27,f33,f31,f29,f27]) ).
fof(f41,plain,
! [X0] : negate(negate(X0)) = X0,
inference(forward_demodulation,[],[f25,f24]) ).
fof(f42,plain,
! [X0,X1] : negate(sF5(X0,X1)) = X0,
inference(forward_demodulation,[],[f22,f21]) ).
fof(f44,plain,
! [X0,X1] : negate(add(sF2(X0,X1),sF4(X0,X1))) = X0,
inference(forward_demodulation,[],[f42,f19]) ).
fof(f46,plain,
! [X0,X1] : negate(add(sF2(X0,X1),negate(sF3(X0,X1)))) = X0,
inference(forward_demodulation,[],[f44,f17]) ).
fof(f47,plain,
! [X0,X1] : negate(add(sF2(X0,X1),negate(add(X0,negate(X1))))) = X0,
inference(forward_demodulation,[],[f46,f15]) ).
fof(f48,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
inference(forward_demodulation,[],[f47,f13]) ).
fof(f50,plain,
b = negate(sF8),
inference(superposition,[],[f41,f27]) ).
fof(f57,plain,
sF9 = add(sF8,a),
inference(superposition,[],[f1,f29]) ).
fof(f58,plain,
sF12 = add(sF8,sF11),
inference(superposition,[],[f1,f35]) ).
fof(f85,plain,
sF8 = negate(add(negate(sF9),negate(add(sF8,negate(a))))),
inference(superposition,[],[f48,f57]) ).
fof(f117,plain,
sF8 = negate(add(negate(sF9),negate(add(sF8,sF11)))),
inference(forward_demodulation,[],[f85,f33]) ).
fof(f124,plain,
sF8 = negate(add(negate(sF9),negate(sF12))),
inference(forward_demodulation,[],[f117,f58]) ).
fof(f130,plain,
sF8 = negate(add(negate(sF9),sF13)),
inference(forward_demodulation,[],[f124,f37]) ).
fof(f132,plain,
sF8 = negate(add(sF13,negate(sF9))),
inference(forward_demodulation,[],[f130,f1]) ).
fof(f134,plain,
sF8 = negate(add(sF13,sF10)),
inference(forward_demodulation,[],[f132,f31]) ).
fof(f136,plain,
sF8 = negate(add(sF10,sF13)),
inference(forward_demodulation,[],[f134,f1]) ).
fof(f138,plain,
sF8 = negate(sF14),
inference(forward_demodulation,[],[f136,f39]) ).
fof(f141,plain,
sF14 = negate(sF8),
inference(superposition,[],[f41,f138]) ).
fof(f142,plain,
b = sF14,
inference(forward_demodulation,[],[f141,f50]) ).
fof(f145,plain,
b != b,
inference(superposition,[],[f40,f142]) ).
fof(f146,plain,
$false,
inference(trivial_inequality_removal,[],[f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 23:29:33 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 3.04/1.10 % (3109464)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.04/1.10 % (3109474)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1486859081:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.04/1.10 % (3109475)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4100330747:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.04/1.10 % (3109472)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2155976571:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.04/1.10 % (3109471)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1348789651:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.04/1.10 % (3109470)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=3236545385:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.04/1.10 % (3109469)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=1954580471:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.04/1.10 % (3109473)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3138745190:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.04/1.10 % (3109473)First to succeed.
% 3.04/1.10 % (3109473)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3109464"
% 3.04/1.10 % (3109474)Also succeeded, but the first one will report.
% 3.04/1.10 % (3109475)Also succeeded, but the first one will report.
% 3.04/1.10 % (3109472)Also succeeded, but the first one will report.
% 3.04/1.10 % (3109473)Refutation found. Thanks to Tanya!
% 3.04/1.10 % SZS status Unsatisfiable for theBenchmark
% 3.04/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.04/1.10 % (3109473)------------------------------
% 3.04/1.10 % (3109473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.10 % (3109473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.10 % (3109473)CaDiCaL version: 2.1.3
% 3.04/1.10 % (3109473)Termination reason: Refutation
% 3.04/1.10 % (3109473)Time elapsed: 0.005 s
% 3.04/1.10 % (3109473)Peak memory usage: 88 MB
% 3.04/1.10 % (3109473)Instructions burned: 6 (million)
% 3.04/1.10 % (3109473)------------------------------
% 3.04/1.10 % (3109473)------------------------------
% 3.04/1.10 % (3109464)Success in time 0.393 s
% 3.04/1.10 % Vampire exiting
%------------------------------------------------------------------------------