%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ROB003-1 : 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 : n007.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 2.38s 1.17s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 78 ( 78 unt; 15 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 80 ( 80 !; 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(f2,negated_conjecture,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_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,axiom,
! [X0] : add(X0,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',there_exists_a_constant) ).
fof(f5,plain,
! [X0] : c = add(X0,c),
inference(reorient_equations,[],[f4]) ).
fof(f6,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(f7,plain,
b != add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = add(add(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = add(X0,add(X1,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
! [X2,X0,X1] : sF0(X0,X1,X2) = sF1(X0,X1,X2),
inference(definition_folding,[],[f2,f11,f9]) ).
fof(f13,definition,
! [X0,X1] : sF2(X0,X1) = negate(add(X0,X1)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f14,plain,
! [X0,X1] : negate(add(X0,X1)) = sF2(X0,X1),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X0,X1] : sF3(X0,X1) = add(X0,negate(X1)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f16,plain,
! [X0,X1] : add(X0,negate(X1)) = sF3(X0,X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
! [X0,X1] : sF4(X0,X1) = negate(sF3(X0,X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f18,plain,
! [X0,X1] : negate(sF3(X0,X1)) = sF4(X0,X1),
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
! [X0,X1] : sF5(X0,X1) = add(sF2(X0,X1),sF4(X0,X1)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f20,plain,
! [X0,X1] : add(sF2(X0,X1),sF4(X0,X1)) = sF5(X0,X1),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
! [X0,X1] : sF6(X0,X1) = negate(sF5(X0,X1)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f22,plain,
! [X0,X1] : negate(sF5(X0,X1)) = sF6(X0,X1),
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
! [X0,X1] : sF6(X0,X1) = X0,
inference(definition_folding,[],[f3,f22,f20,f18,f16,f14]) ).
fof(f24,definition,
! [X0] : sF7(X0) = add(X0,c),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f25,plain,
! [X0] : add(X0,c) = sF7(X0),
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
! [X0] : c = sF7(X0),
inference(definition_folding,[],[f5,f25]) ).
fof(f27,definition,
sF8 = negate(b),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f28,plain,
negate(b) = sF8,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF9 = add(a,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f30,plain,
add(a,sF8) = sF9,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF10 = negate(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f32,plain,
negate(sF9) = sF10,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF11 = negate(a),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f34,plain,
negate(a) = sF11,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF12 = add(sF11,sF8),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f36,plain,
add(sF11,sF8) = sF12,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF13 = negate(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f38,plain,
negate(sF12) = sF13,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF14 = add(sF10,sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f40,plain,
add(sF10,sF13) = sF14,
inference(reorient_equations,[],[f39]) ).
fof(f41,plain,
b != sF14,
inference(definition_folding,[],[f7,f40,f38,f36,f28,f34,f32,f30,f28]) ).
fof(f42,plain,
! [X0] : c = add(X0,c),
inference(forward_demodulation,[],[f26,f25]) ).
fof(f43,plain,
! [X0,X1] : negate(sF5(X0,X1)) = X0,
inference(forward_demodulation,[],[f23,f22]) ).
fof(f44,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = sF0(X0,X1,X2),
inference(forward_demodulation,[],[f12,f11]) ).
fof(f45,plain,
! [X0,X1] : negate(add(sF2(X0,X1),sF4(X0,X1))) = X0,
inference(forward_demodulation,[],[f43,f20]) ).
fof(f46,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(forward_demodulation,[],[f44,f9]) ).
fof(f47,plain,
! [X0,X1] : negate(add(sF2(X0,X1),negate(sF3(X0,X1)))) = X0,
inference(forward_demodulation,[],[f45,f18]) ).
fof(f48,plain,
! [X0,X1] : negate(add(sF2(X0,X1),negate(add(X0,negate(X1))))) = X0,
inference(forward_demodulation,[],[f47,f16]) ).
fof(f49,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
inference(forward_demodulation,[],[f48,f14]) ).
fof(f50,plain,
! [X0] : c = add(c,X0),
inference(superposition,[],[f1,f42]) ).
fof(f51,plain,
sF9 = add(sF8,a),
inference(superposition,[],[f1,f30]) ).
fof(f52,plain,
sF12 = add(sF8,sF11),
inference(superposition,[],[f1,f36]) ).
fof(f90,plain,
! [X0] : negate(add(negate(c),negate(add(X0,negate(c))))) = X0,
inference(superposition,[],[f49,f42]) ).
fof(f91,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X1,negate(X0))))) = X1,
inference(superposition,[],[f49,f1]) ).
fof(f94,plain,
! [X0] : c = negate(add(negate(c),negate(add(c,negate(X0))))),
inference(superposition,[],[f49,f50]) ).
fof(f96,plain,
sF8 = negate(add(negate(sF9),negate(add(sF8,negate(a))))),
inference(superposition,[],[f49,f51]) ).
fof(f118,plain,
sF8 = negate(add(negate(sF9),negate(add(sF8,sF11)))),
inference(forward_demodulation,[],[f96,f34]) ).
fof(f120,plain,
c = negate(add(negate(c),negate(c))),
inference(forward_demodulation,[],[f94,f50]) ).
fof(f124,plain,
sF8 = negate(add(negate(sF9),negate(sF12))),
inference(forward_demodulation,[],[f118,f52]) ).
fof(f126,plain,
sF8 = negate(add(negate(sF9),sF13)),
inference(forward_demodulation,[],[f124,f38]) ).
fof(f127,plain,
sF8 = negate(add(sF13,negate(sF9))),
inference(forward_demodulation,[],[f126,f1]) ).
fof(f128,plain,
sF8 = negate(add(sF13,sF10)),
inference(forward_demodulation,[],[f127,f32]) ).
fof(f129,plain,
sF8 = negate(add(sF10,sF13)),
inference(forward_demodulation,[],[f128,f1]) ).
fof(f130,plain,
sF8 = negate(sF14),
inference(forward_demodulation,[],[f129,f40]) ).
fof(f1156,plain,
! [X0] : negate(add(negate(c),negate(add(negate(c),X0)))) = X0,
inference(superposition,[],[f90,f1]) ).
fof(f1972,plain,
! [X0] : negate(add(X0,negate(c))) = negate(add(negate(c),X0)),
inference(superposition,[],[f1156,f90]) ).
fof(f2340,plain,
! [X0] : negate(add(negate(add(add(negate(c),negate(c)),X0)),negate(add(X0,c)))) = X0,
inference(superposition,[],[f91,f120]) ).
fof(f2428,plain,
! [X0] : negate(add(negate(add(add(negate(c),negate(c)),X0)),negate(c))) = X0,
inference(forward_demodulation,[],[f2340,f42]) ).
fof(f2507,plain,
! [X0] : negate(add(negate(c),negate(add(add(negate(c),negate(c)),X0)))) = X0,
inference(forward_demodulation,[],[f2428,f1972]) ).
fof(f2531,plain,
! [X0] : negate(add(negate(c),negate(add(negate(c),add(negate(c),X0))))) = X0,
inference(forward_demodulation,[],[f2507,f46]) ).
fof(f2542,plain,
! [X0] : add(negate(c),X0) = X0,
inference(forward_demodulation,[],[f2531,f1156]) ).
fof(f2572,plain,
! [X0] : negate(add(negate(c),negate(X0))) = X0,
inference(superposition,[],[f1156,f2542]) ).
fof(f2641,plain,
! [X0] : negate(negate(X0)) = X0,
inference(forward_demodulation,[],[f2572,f2542]) ).
fof(f2698,plain,
b = negate(sF8),
inference(superposition,[],[f2641,f28]) ).
fof(f2701,plain,
sF14 = negate(sF8),
inference(superposition,[],[f2641,f130]) ).
fof(f2736,plain,
b = sF14,
inference(forward_demodulation,[],[f2701,f2698]) ).
fof(f2737,plain,
b != b,
inference(superposition,[],[f41,f2736]) ).
fof(f2743,plain,
$false,
inference(trivial_inequality_removal,[],[f2737]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 23:23:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 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
% 2.38/1.17 % (1885116)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.38/1.17 % (1885125)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2098163823:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.38/1.17 % (1885125)First to succeed.
% 2.38/1.17 % (1885125)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1885116"
% 2.38/1.17 % (1885123)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2264211887:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.38/1.17 % (1885121)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=874724145:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.38/1.17 % (1885122)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=2295070162:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.38/1.17 % (1885124)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1901498592:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.38/1.17 % (1885127)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1031350342:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.38/1.17 % (1885126)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2329045212:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.38/1.17 % (1885126)Also succeeded, but the first one will report.
% 2.38/1.17 % (1885124)Instruction limit reached!
% 2.38/1.17 % (1885124)------------------------------
% 2.38/1.17 % (1885124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/1.17 % (1885124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/1.17 % (1885124)CaDiCaL version: 2.1.3
% 2.38/1.17 % (1885124)Termination reason: Instruction limit
% 2.38/1.17 % (1885124)Termination phase: Saturation
% 2.38/1.17 % (1885124)Time elapsed: 0.080 s
% 2.38/1.17 % (1885124)Peak memory usage: 88 MB
% 2.38/1.17 % (1885124)Instructions burned: 137 (million)
% 2.38/1.17 % (1885125)Refutation found. Thanks to Tanya!
% 2.38/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.38/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.36 % (1885125)------------------------------
% 2.81/1.36 % (1885125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.36 % (1885125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.36 % (1885125)CaDiCaL version: 2.1.3
% 2.81/1.36 % (1885125)Termination reason: Refutation
% 2.81/1.36 % (1885125)Time elapsed: 0.029 s
% 2.81/1.36 % (1885125)Peak memory usage: 89 MB
% 2.81/1.36 % (1885125)Instructions burned: 98 (million)
% 2.81/1.36 % (1885125)------------------------------
% 2.81/1.36 % (1885125)------------------------------
% 2.81/1.36 % (1885116)Success in time 0.314 s
% 2.81/1.36 % Vampire exiting
%------------------------------------------------------------------------------