%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 09:36:09 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',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/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
fof(f10,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f12,plain,
x != inverse(inverse(x)),
inference(reorient_equations,[],[f11]) ).
fof(f16,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f5,f1]) ).
fof(f26,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[],[f6,f2]) ).
fof(f29,plain,
! [X0,X1] : add(X0,multiply(additive_identity,X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[],[f3,f5]) ).
fof(f30,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[],[f3,f8]) ).
fof(f47,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f30,f26]) ).
fof(f55,plain,
! [X0,X1] : add(additive_identity,multiply(X0,X1)) = multiply(X0,add(inverse(X0),X1)),
inference(superposition,[],[f4,f10]) ).
fof(f61,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(superposition,[],[f4,f10]) ).
fof(f73,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,add(X1,inverse(X0))),
inference(forward_demodulation,[],[f61,f5]) ).
fof(f76,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,add(inverse(X0),X1)),
inference(forward_demodulation,[],[f55,f16]) ).
fof(f114,plain,
! [X0] : add(X0,additive_identity) = add(X0,inverse(inverse(X0))),
inference(superposition,[],[f47,f10]) ).
fof(f125,plain,
! [X0] : add(X0,inverse(inverse(X0))) = X0,
inference(forward_demodulation,[],[f114,f5]) ).
fof(f142,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(X0,additive_identity),
inference(superposition,[],[f73,f16]) ).
fof(f157,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[],[f142,f10]) ).
fof(f171,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(superposition,[],[f2,f157]) ).
fof(f181,plain,
! [X0] : multiply(X0,multiplicative_identity) = multiply(X0,inverse(inverse(X0))),
inference(superposition,[],[f76,f8]) ).
fof(f192,plain,
! [X0] : multiply(X0,inverse(inverse(X0))) = X0,
inference(forward_demodulation,[],[f181,f6]) ).
fof(f208,plain,
! [X0,X1] : add(X1,multiply(additive_identity,X0)) = multiply(X1,add(X0,X1)),
inference(superposition,[],[f29,f1]) ).
fof(f236,plain,
! [X0,X1] : add(X1,additive_identity) = multiply(X1,add(X0,X1)),
inference(forward_demodulation,[],[f208,f171]) ).
fof(f248,plain,
! [X0,X1] : multiply(X1,add(X0,X1)) = X1,
inference(forward_demodulation,[],[f236,f5]) ).
fof(f772,plain,
! [X0] : inverse(inverse(X0)) = multiply(inverse(inverse(X0)),X0),
inference(superposition,[],[f248,f125]) ).
fof(f806,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(inverse(X0))),
inference(forward_demodulation,[],[f772,f2]) ).
fof(f814,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f806,f192]) ).
fof(f926,plain,
x != x,
inference(superposition,[],[f12,f814]) ).
fof(f937,plain,
$false,
inference(trivial_inequality_removal,[],[f926]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n011.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:04:00 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 Running first-order model finding
% 0.09/0.19 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25 % (3785479)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (3785486)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2010419327:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (3785485)% WARNING: option uhcvi not known.
% 0.09/0.25 % (3785484)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1600806060_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.25 % (3785485)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=274090672:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (3785487)dis+10_1_sil=32000:sp=arity:random_seed=3391385261:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (3785488)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=220680940:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (3785489)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1034015878:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.25 % (3785490)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1398949471:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % TRYING [1]
% 0.09/0.25 % TRYING [2]
% 0.09/0.25 % TRYING [3]
% 0.09/0.25 % TRYING [4]
% 0.09/0.25 % TRYING [5]
% 0.09/0.25 % (3785488) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3785479-3785488"...
% 0.09/0.25 % (3785488)...printing done.
% 0.09/0.25 % (3785488)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (3785488)------------------------------
% 0.09/0.25 % (3785488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (3785488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (3785488)CaDiCaL version: 2.1.3
% 0.09/0.25 % (3785488)Termination reason: Refutation
% 0.09/0.25 % (3785488)Time elapsed: 0.017 s
% 0.09/0.25 % (3785488)Peak memory usage: 11 MB
% 0.09/0.25 % (3785488)Instructions burned: 28 (million)
% 0.09/0.25 % (3785479)Success in time 0.05 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------