%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ROB008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:36:15 PM UTC 2026
% Result : Unsatisfiable 2.66s 1.24s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 68 ( 68 unt; 16 def)
% Number of atoms : 68 ( 67 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-3 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
fof(f4,negated_conjecture,
negate(add(a,negate(add(b,c)))) = negate(add(a,add(b,negate(c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
fof(f5,negated_conjecture,
add(a,b) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_result) ).
fof(f6,plain,
a != add(a,b),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = add(add(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f8,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = add(X0,add(X1,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,plain,
! [X2,X0,X1] : sF0(X0,X1,X2) = sF1(X0,X1,X2),
inference(definition_folding,[],[f2,f10,f8]) ).
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,
sF7 = add(b,c),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f24,plain,
add(b,c) = sF7,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF8 = negate(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f26,plain,
negate(sF7) = sF8,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF9 = add(a,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f28,plain,
add(a,sF8) = sF9,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF10 = negate(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f30,plain,
negate(sF9) = sF10,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF11 = negate(c),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f32,plain,
negate(c) = sF11,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF12 = add(b,sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f34,plain,
add(b,sF11) = sF12,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF13 = add(a,sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f36,plain,
add(a,sF12) = sF13,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF14 = negate(sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f38,plain,
negate(sF13) = sF14,
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
sF10 = sF14,
inference(definition_folding,[],[f4,f38,f36,f34,f32,f30,f28,f26,f24]) ).
fof(f40,definition,
sF15 = add(a,b),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f41,plain,
add(a,b) = sF15,
inference(reorient_equations,[],[f40]) ).
fof(f42,plain,
a != sF15,
inference(definition_folding,[],[f6,f41]) ).
fof(f43,plain,
! [X0,X1] : negate(sF5(X0,X1)) = X0,
inference(forward_demodulation,[],[f22,f21]) ).
fof(f44,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = sF0(X0,X1,X2),
inference(forward_demodulation,[],[f11,f10]) ).
fof(f45,plain,
! [X0,X1] : negate(add(sF2(X0,X1),sF4(X0,X1))) = X0,
inference(forward_demodulation,[],[f43,f19]) ).
fof(f46,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(forward_demodulation,[],[f44,f8]) ).
fof(f47,plain,
! [X0,X1] : negate(add(sF2(X0,X1),negate(sF3(X0,X1)))) = X0,
inference(forward_demodulation,[],[f45,f17]) ).
fof(f48,plain,
! [X0,X1] : negate(add(sF2(X0,X1),negate(add(X0,negate(X1))))) = X0,
inference(forward_demodulation,[],[f47,f15]) ).
fof(f49,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
inference(forward_demodulation,[],[f48,f13]) ).
fof(f53,plain,
! [X0] : add(a,add(b,X0)) = add(sF15,X0),
inference(superposition,[],[f46,f41]) ).
fof(f163,plain,
! [X0] : negate(add(negate(add(X0,c)),negate(add(X0,sF11)))) = X0,
inference(superposition,[],[f49,f32]) ).
fof(f164,plain,
! [X0] : negate(add(negate(add(X0,sF7)),negate(add(X0,sF8)))) = X0,
inference(superposition,[],[f49,f26]) ).
fof(f2048,plain,
sF15 = negate(add(negate(add(a,add(b,c))),negate(add(sF15,sF11)))),
inference(superposition,[],[f163,f53]) ).
fof(f2070,plain,
sF15 = negate(add(negate(add(a,add(b,c))),negate(add(a,add(b,sF11))))),
inference(forward_demodulation,[],[f2048,f53]) ).
fof(f2085,plain,
sF15 = negate(add(negate(add(a,add(b,c))),negate(add(a,sF12)))),
inference(forward_demodulation,[],[f2070,f34]) ).
fof(f2098,plain,
sF15 = negate(add(negate(add(a,sF12)),negate(add(a,add(b,c))))),
inference(forward_demodulation,[],[f2085,f1]) ).
fof(f2107,plain,
sF15 = negate(add(negate(add(a,sF12)),negate(add(a,sF7)))),
inference(forward_demodulation,[],[f2098,f24]) ).
fof(f2113,plain,
sF15 = negate(add(negate(add(a,sF7)),negate(add(a,sF12)))),
inference(forward_demodulation,[],[f2107,f1]) ).
fof(f2117,plain,
sF15 = negate(add(negate(add(a,sF7)),negate(sF13))),
inference(forward_demodulation,[],[f2113,f36]) ).
fof(f2121,plain,
sF15 = negate(add(negate(sF13),negate(add(a,sF7)))),
inference(forward_demodulation,[],[f2117,f1]) ).
fof(f2125,plain,
sF15 = negate(add(sF14,negate(add(a,sF7)))),
inference(forward_demodulation,[],[f2121,f38]) ).
fof(f2129,plain,
sF15 = negate(add(sF10,negate(add(a,sF7)))),
inference(forward_demodulation,[],[f2125,f39]) ).
fof(f2453,plain,
a = negate(add(negate(add(a,sF7)),negate(sF9))),
inference(superposition,[],[f164,f28]) ).
fof(f2469,plain,
a = negate(add(negate(sF9),negate(add(a,sF7)))),
inference(forward_demodulation,[],[f2453,f1]) ).
fof(f2486,plain,
a = negate(add(sF10,negate(add(a,sF7)))),
inference(forward_demodulation,[],[f2469,f30]) ).
fof(f2498,plain,
a = sF15,
inference(forward_demodulation,[],[f2486,f2129]) ).
fof(f2540,plain,
a != a,
inference(superposition,[],[f42,f2498]) ).
fof(f2546,plain,
$false,
inference(trivial_inequality_removal,[],[f2540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 23:26:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.66/1.24 % (3522909)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.66/1.24 % (3522918)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3889666137:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.66/1.24 % (3522918)First to succeed.
% 2.66/1.24 % (3522920)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=219746652:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.66/1.24 % (3522919)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2643148095:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.66/1.24 % (3522917)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4204043557:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.66/1.24 % (3522916)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2813884885:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.66/1.24 % (3522914)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=723281362:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.66/1.24 % (3522915)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=2030303431:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.66/1.24 % (3522918)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3522909"
% 2.66/1.24 % (3522917)Also succeeded, but the first one will report.
% 2.66/1.24 % (3522920)Also succeeded, but the first one will report.
% 2.66/1.24 % (3522919)Also succeeded, but the first one will report.
% 2.66/1.24 % (3522918)Refutation found. Thanks to Tanya!
% 2.66/1.24 % SZS status Unsatisfiable for theBenchmark
% 2.66/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.24 % (3522918)------------------------------
% 2.66/1.24 % (3522918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.24 % (3522918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.24 % (3522918)CaDiCaL version: 2.1.3
% 2.66/1.24 % (3522918)Termination reason: Refutation
% 2.66/1.24 % (3522918)Time elapsed: 0.027 s
% 2.66/1.24 % (3522918)Peak memory usage: 89 MB
% 2.66/1.24 % (3522918)Instructions burned: 95 (million)
% 2.66/1.24 % (3522918)------------------------------
% 2.66/1.24 % (3522918)------------------------------
% 2.66/1.24 % (3522909)Success in time 0.308 s
% 2.66/1.24 % Vampire exiting
%------------------------------------------------------------------------------