%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 09:36:07 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',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/Axioms/BOO004-0.ax',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_operation) ).
fof(f12,plain,
a != multiply(a,add(a,b)),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f1,f5]) ).
fof(f25,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[],[f2,f6]) ).
fof(f37,plain,
! [X0,X1] : add(X0,multiply(additive_identity,X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[],[f3,f5]) ).
fof(f43,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(superposition,[],[f3,f8]) ).
fof(f52,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(X1,inverse(X0))),
inference(forward_demodulation,[],[f43,f6]) ).
fof(f61,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[],[f52,f25]) ).
fof(f70,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[],[f61,f8]) ).
fof(f76,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(superposition,[],[f70,f1]) ).
fof(f147,plain,
a != add(a,multiply(additive_identity,b)),
inference(superposition,[],[f12,f37]) ).
fof(f417,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(multiplicative_identity,X1)),
inference(superposition,[],[f4,f6]) ).
fof(f459,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[],[f417,f76]) ).
fof(f465,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f459,f6]) ).
fof(f488,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(superposition,[],[f465,f13]) ).
fof(f509,plain,
a != add(a,additive_identity),
inference(superposition,[],[f147,f488]) ).
fof(f536,plain,
$false,
inference(forward_subsumption_resolution,[],[f509,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:05:27 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.27 % (2016817)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (2016824)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=181016367:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (2016823)% WARNING: option uhcvi not known.
% 0.19/0.27 % (2016823)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=862622394:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (2016822)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2125773482_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (2016825)dis+10_1_sil=32000:sp=arity:random_seed=2559353694:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (2016826)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1848176964:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (2016824) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2016817-2016824"...
% 0.19/0.27 % (2016827)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3564387457:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (2016824)...printing done.
% 0.19/0.27 % TRYING [1]
% 0.19/0.27 % TRYING [2]
% 0.19/0.27 % (2016824)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (2016824)------------------------------
% 0.19/0.27 % (2016824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2016824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2016824)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2016824)Termination reason: Refutation
% 0.19/0.27 % (2016824)Time elapsed: 0.008 s
% 0.19/0.27 % (2016824)Peak memory usage: 11 MB
% 0.19/0.27 % (2016824)Instructions burned: 22 (million)
% 0.19/0.27 % (2016817)Success in time 0.033 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------