%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:35:52 AM UTC 2026
% Result : Unsatisfiable 2.98s 1.26s
% Output : Refutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 56 unt; 1 def)
% Number of atoms : 56 ( 52 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
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',distributivity2) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f10,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_a_multiplicative_identity) ).
fof(f12,plain,
multiplicative_identity = add(a,b),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_an_additive_identity) ).
fof(f14,plain,
additive_identity = multiply(a,b),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
b != inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_is_b) ).
fof(f16,definition,
~ sP0(inverse(a)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f17,plain,
sP0(b),
inference(inequality_splitting,[],[f15,f16]) ).
fof(f18,plain,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = add(multiply(add(X0,X1),X0),multiply(add(X0,X1),X2)),
inference(forward_demodulation,[],[f3,f4]) ).
fof(f22,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f5,f1]) ).
fof(f33,plain,
! [X0] : multiply(X0,multiplicative_identity) = add(multiply(X0,a),multiply(X0,b)),
inference(superposition,[],[f4,f12]) ).
fof(f34,plain,
! [X0,X1] : multiply(X1,X0) = add(multiply(X1,X0),multiply(X1,additive_identity)),
inference(superposition,[],[f4,f5]) ).
fof(f35,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),multiply(X0,inverse(X1))),
inference(superposition,[],[f4,f8]) ).
fof(f43,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(forward_demodulation,[],[f35,f6]) ).
fof(f44,plain,
! [X0] : add(multiply(X0,a),multiply(X0,b)) = X0,
inference(forward_demodulation,[],[f33,f6]) ).
fof(f51,plain,
! [X0,X1] : add(X0,multiply(additive_identity,X1)) = add(multiply(X0,X0),multiply(X0,X1)),
inference(superposition,[],[f18,f5]) ).
fof(f59,plain,
! [X2,X0,X1] : add(X1,multiply(X2,X0)) = add(multiply(add(X1,X2),X1),multiply(X0,add(X1,X2))),
inference(superposition,[],[f18,f2]) ).
fof(f72,plain,
! [X2,X0,X1] : add(X1,multiply(X2,X0)) = add(multiply(add(X1,X2),X1),add(multiply(X0,X1),multiply(X0,X2))),
inference(forward_demodulation,[],[f59,f4]) ).
fof(f130,plain,
! [X0] : add(multiply(X0,X0),additive_identity) = X0,
inference(superposition,[],[f43,f10]) ).
fof(f139,plain,
! [X0] : multiply(X0,X0) = X0,
inference(forward_demodulation,[],[f130,f5]) ).
fof(f148,plain,
! [X0,X1] : add(X0,multiply(additive_identity,X1)) = add(X0,multiply(X0,X1)),
inference(backward_demodulation,[],[f51,f139]) ).
fof(f201,plain,
! [X0] : additive_identity = add(additive_identity,multiply(X0,additive_identity)),
inference(superposition,[],[f34,f10]) ).
fof(f210,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,additive_identity)),
inference(superposition,[],[f18,f34]) ).
fof(f222,plain,
! [X2,X0,X1] : add(X1,multiply(X2,X0)) = add(add(X1,multiply(X2,additive_identity)),add(multiply(X0,X1),multiply(X0,X2))),
inference(backward_demodulation,[],[f72,f210]) ).
fof(f224,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[],[f201,f22]) ).
fof(f240,plain,
! [X2,X0,X1] : add(X1,multiply(X2,X0)) = add(add(X1,additive_identity),add(multiply(X0,X1),multiply(X0,X2))),
inference(backward_demodulation,[],[f222,f224]) ).
fof(f243,plain,
! [X2,X0,X1] : add(X1,multiply(X2,X0)) = add(X1,add(multiply(X0,X1),multiply(X0,X2))),
inference(forward_demodulation,[],[f240,f5]) ).
fof(f261,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(superposition,[],[f2,f224]) ).
fof(f263,plain,
! [X0,X1] : add(X0,additive_identity) = add(X0,multiply(X0,X1)),
inference(backward_demodulation,[],[f148,f261]) ).
fof(f265,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f263,f5]) ).
fof(f311,plain,
! [X0,X1] : add(X1,multiply(X0,X1)) = X1,
inference(superposition,[],[f265,f2]) ).
fof(f876,plain,
! [X0,X1] : add(X0,add(multiply(X1,X0),additive_identity)) = add(X0,multiply(inverse(X1),X1)),
inference(superposition,[],[f243,f10]) ).
fof(f882,plain,
! [X0] : add(X0,multiply(b,a)) = add(X0,add(multiply(a,X0),additive_identity)),
inference(superposition,[],[f243,f14]) ).
fof(f946,plain,
! [X0] : add(X0,multiply(b,a)) = add(X0,multiply(a,X0)),
inference(forward_demodulation,[],[f882,f5]) ).
fof(f952,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = add(X0,multiply(inverse(X1),X1)),
inference(forward_demodulation,[],[f876,f5]) ).
fof(f993,plain,
! [X0] : add(X0,multiply(b,a)) = X0,
inference(forward_demodulation,[],[f946,f311]) ).
fof(f996,plain,
! [X0,X1] : add(X0,multiply(inverse(X1),X1)) = X0,
inference(forward_demodulation,[],[f952,f311]) ).
fof(f1045,plain,
additive_identity = multiply(b,a),
inference(superposition,[],[f22,f993]) ).
fof(f1193,plain,
b = add(additive_identity,multiply(b,inverse(a))),
inference(superposition,[],[f43,f1045]) ).
fof(f1201,plain,
b = multiply(b,inverse(a)),
inference(forward_demodulation,[],[f1193,f22]) ).
fof(f1361,plain,
b = multiply(inverse(a),b),
inference(superposition,[],[f2,f1201]) ).
fof(f1537,plain,
inverse(a) = add(multiply(inverse(a),a),b),
inference(superposition,[],[f44,f1361]) ).
fof(f1664,plain,
! [X0] : additive_identity = multiply(inverse(X0),X0),
inference(superposition,[],[f22,f996]) ).
fof(f1666,plain,
inverse(a) = add(additive_identity,b),
inference(backward_demodulation,[],[f1537,f1664]) ).
fof(f1692,plain,
b = inverse(a),
inference(forward_demodulation,[],[f1666,f22]) ).
fof(f1713,plain,
sP0(inverse(a)),
inference(backward_demodulation,[],[f17,f1692]) ).
fof(f1784,plain,
$false,
inference(forward_subsumption_resolution,[],[f1713,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n002.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Mon Sep 28 21:06:37 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running first-order theorem proving
% 0.11/0.23 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
% 2.98/1.26 % (761373)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.98/1.26 % (761416)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=385409198:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.98/1.26 % (761415)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3782438473:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.98/1.26 % (761413)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=2206442771:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.98/1.26 % (761412)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=3746269678:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.98/1.26 % (761416)First to succeed.
% 2.98/1.26 % (761416)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-761373"
% 2.98/1.26 % (761421)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=959483716:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.98/1.26 % (761420)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1338514567:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.98/1.26 % (761418)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4162395613:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.98/1.26 % (761421)Also succeeded, but the first one will report.
% 2.98/1.26 % (761418)Also succeeded, but the first one will report.
% 2.98/1.26 % (761420)Also succeeded, but the first one will report.
% 2.98/1.26 % (761416)Refutation found. Thanks to Tanya!
% 2.98/1.26 % SZS status Unsatisfiable for theBenchmark
% 2.98/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 2.98/1.26 % (761416)------------------------------
% 2.98/1.26 % (761416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.26 % (761416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.26 % (761416)CaDiCaL version: 2.1.3
% 2.98/1.26 % (761416)Termination reason: Refutation
% 2.98/1.26 % (761416)Time elapsed: 0.036 s
% 2.98/1.26 % (761416)Peak memory usage: 88 MB
% 2.98/1.26 % (761416)Instructions burned: 88 (million)
% 2.98/1.26 % (761416)------------------------------
% 2.98/1.26 % (761416)------------------------------
% 2.98/1.26 % (761373)Success in time 0.339 s
% 2.98/1.26 % Vampire exiting
%------------------------------------------------------------------------------