%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG008-4 : 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 : 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 12:35:06 PM UTC 2026
% Result : Unsatisfiable 4.76s 2.14s
% Output : Refutation 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 60 unt; 4 def)
% Number of atoms : 60 ( 59 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).
fof(f3,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
fof(f14,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse1) ).
fof(f15,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse2) ).
fof(f16,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_addition) ).
fof(f18,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutative_addition) ).
fof(f20,axiom,
! [X0] : multiply(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
fof(f21,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f22,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
fof(f23,plain,
c != multiply(b,a),
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
! [X0] : sF0(X0) = add(additive_identity,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f25,plain,
! [X0] : add(additive_identity,X0) = sF0(X0),
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f25]) ).
fof(f27,definition,
! [X0] : sF1(X0) = add(additive_inverse(X0),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f28,plain,
! [X0] : add(additive_inverse(X0),X0) = sF1(X0),
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
! [X0] : additive_identity = sF1(X0),
inference(definition_folding,[],[f3,f28]) ).
fof(f39,definition,
sF5 = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f40,plain,
multiply(a,b) = sF5,
inference(reorient_equations,[],[f39]) ).
fof(f41,plain,
c = sF5,
inference(definition_folding,[],[f21,f40]) ).
fof(f42,definition,
sF6 = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f43,plain,
multiply(b,a) = sF6,
inference(reorient_equations,[],[f42]) ).
fof(f44,plain,
c != sF6,
inference(definition_folding,[],[f23,f43]) ).
fof(f47,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(forward_demodulation,[],[f29,f28]) ).
fof(f48,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(forward_demodulation,[],[f26,f25]) ).
fof(f49,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(forward_demodulation,[],[f47,f18]) ).
fof(f90,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(superposition,[],[f48,f18]) ).
fof(f117,plain,
! [X0,X1] : add(additive_identity,X1) = add(X0,add(additive_inverse(X0),X1)),
inference(superposition,[],[f17,f49]) ).
fof(f122,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f117,f48]) ).
fof(f137,plain,
! [X2,X0,X1] : add(multiply(X0,X1),add(multiply(additive_inverse(X0),X1),X2)) = X2,
inference(superposition,[],[f122,f16]) ).
fof(f166,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[],[f4,f20]) ).
fof(f168,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[],[f5,f20]) ).
fof(f169,plain,
! [X0,X1] : multiply(add(X1,X0),X0) = add(multiply(X1,X0),X0),
inference(superposition,[],[f5,f20]) ).
fof(f174,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X1,X0),X0),
inference(forward_demodulation,[],[f169,f18]) ).
fof(f331,plain,
! [X0,X1] : add(multiply(X0,X1),additive_identity) = additive_inverse(multiply(additive_inverse(X0),X1)),
inference(superposition,[],[f137,f49]) ).
fof(f345,plain,
! [X0,X1] : add(multiply(X0,X1),additive_identity) = multiply(additive_inverse(X0),additive_inverse(X1)),
inference(forward_demodulation,[],[f331,f14]) ).
fof(f359,plain,
! [X0,X1] : add(additive_identity,multiply(X0,X1)) = multiply(additive_inverse(X0),additive_inverse(X1)),
inference(forward_demodulation,[],[f345,f18]) ).
fof(f370,plain,
! [X0,X1] : multiply(X0,X1) = multiply(additive_inverse(X0),additive_inverse(X1)),
inference(forward_demodulation,[],[f359,f48]) ).
fof(f395,plain,
! [X0] : additive_inverse(X0) = multiply(X0,X0),
inference(superposition,[],[f20,f370]) ).
fof(f396,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[],[f395,f20]) ).
fof(f416,plain,
! [X0] : additive_identity = add(X0,X0),
inference(superposition,[],[f49,f396]) ).
fof(f417,plain,
! [X0,X1] : add(X0,add(X0,X1)) = X1,
inference(superposition,[],[f122,f396]) ).
fof(f3560,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = multiply(add(X1,X0),X0),
inference(forward_demodulation,[],[f174,f168]) ).
fof(f5162,plain,
! [X0,X1] : multiply(add(X1,X0),add(add(X1,X0),X0)) = add(add(X1,X0),multiply(add(X0,X1),X0)),
inference(superposition,[],[f166,f3560]) ).
fof(f5173,plain,
! [X0,X1] : multiply(add(X1,X0),add(add(X1,X0),X0)) = add(X1,add(X0,multiply(add(X0,X1),X0))),
inference(forward_demodulation,[],[f5162,f17]) ).
fof(f5204,plain,
! [X0,X1] : multiply(add(X1,X0),add(add(X1,X0),X0)) = add(X1,multiply(add(X0,add(X0,X1)),X0)),
inference(forward_demodulation,[],[f5173,f168]) ).
fof(f5225,plain,
! [X0,X1] : multiply(add(X1,X0),add(add(X1,X0),X0)) = add(X1,multiply(X1,X0)),
inference(forward_demodulation,[],[f5204,f417]) ).
fof(f5238,plain,
! [X0,X1] : multiply(X1,add(X1,X0)) = multiply(add(X1,X0),add(add(X1,X0),X0)),
inference(forward_demodulation,[],[f5225,f166]) ).
fof(f5241,plain,
! [X0,X1] : multiply(X1,add(X1,X0)) = multiply(add(X1,X0),add(X1,add(X0,X0))),
inference(forward_demodulation,[],[f5238,f17]) ).
fof(f5243,plain,
! [X0,X1] : multiply(X1,add(X1,X0)) = multiply(add(X1,X0),add(X1,additive_identity)),
inference(forward_demodulation,[],[f5241,f416]) ).
fof(f5244,plain,
! [X0,X1] : multiply(add(X1,X0),X1) = multiply(X1,add(X1,X0)),
inference(forward_demodulation,[],[f5243,f90]) ).
fof(f5252,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f5244,f122]) ).
fof(f5575,plain,
multiply(a,b) = sF6,
inference(superposition,[],[f43,f5252]) ).
fof(f5593,plain,
sF5 = sF6,
inference(forward_demodulation,[],[f5575,f40]) ).
fof(f5696,plain,
c = sF6,
inference(forward_demodulation,[],[f5593,f41]) ).
fof(f5764,plain,
c != c,
inference(superposition,[],[f44,f5696]) ).
fof(f5791,plain,
$false,
inference(trivial_inequality_removal,[],[f5764]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n015.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 27 23:01:46 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.51 Running first-order theorem proving
% 0.24/0.51 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
% 4.76/2.14 % (2111985)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.76/2.14 % (2112002)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=574754910:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.76/2.14 % (2111998)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=3663534008:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.76/2.14 % (2111999)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=960584233:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.76/2.14 % (2112002)First to succeed.
% 4.76/2.14 % (2112002)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2111985"
% 4.76/2.14 % (2112001)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1835840100:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.76/2.14 % (2112000)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1179565544:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.76/2.14 % (2112003)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3061900060:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.76/2.14 % (2112004)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1871256430:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.76/2.14 % (2112003)Also succeeded, but the first one will report.
% 4.76/2.14 % (2112004)Also succeeded, but the first one will report.
% 4.76/2.14 % (2112001)Instruction limit reached!
% 4.76/2.14 % (2112001)------------------------------
% 4.76/2.14 % (2112001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.76/2.14 % (2112001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.76/2.14 % (2112001)CaDiCaL version: 2.1.3
% 4.76/2.14 % (2112001)Termination reason: Instruction limit
% 4.76/2.14 % (2112001)Termination phase: Saturation
% 4.76/2.14 % (2112001)Time elapsed: 0.124 s
% 4.76/2.14 % (2112001)Peak memory usage: 89 MB
% 4.76/2.14 % (2112001)Instructions burned: 136 (million)
% 4.76/2.14 % (2112002)Refutation found. Thanks to Tanya!
% 4.76/2.14 % SZS status Unsatisfiable for theBenchmark
% 4.76/2.14 % SZS output start Proof for theBenchmark
% See solution above
% 4.76/2.14 % (2112002)------------------------------
% 4.76/2.14 % (2112002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.76/2.14 % (2112002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.76/2.14 % (2112002)CaDiCaL version: 2.1.3
% 4.76/2.14 % (2112002)Termination reason: Refutation
% 4.76/2.14 % (2112002)Time elapsed: 0.071 s
% 4.76/2.14 % (2112002)Peak memory usage: 90 MB
% 4.76/2.14 % (2112002)Instructions burned: 152 (million)
% 4.76/2.14 % (2112002)------------------------------
% 4.76/2.14 % (2112002)------------------------------
% 4.76/2.14 % (2111985)Success in time 0.541 s
% 4.76/2.14 % Vampire exiting
%------------------------------------------------------------------------------