%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG007-4 : 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 : n007.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 12:35:05 PM UTC 2026
% Result : Unsatisfiable 4.53s 1.65s
% Output : Refutation 4.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 19 unt; 1 def)
% Number of atoms : 19 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f8,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
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(f20,axiom,
! [X0] : multiply(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
fof(f21,negated_conjecture,
add(a,a) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse) ).
fof(f22,plain,
additive_identity != add(a,a),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
~ sP0(add(a,a)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f24,plain,
sP0(additive_identity),
inference(inequality_splitting,[],[f22,f23]) ).
fof(f27,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(superposition,[],[f3,f8]) ).
fof(f46,plain,
! [X0] : additive_inverse(X0) = additive_inverse(multiply(additive_inverse(X0),X0)),
inference(superposition,[],[f20,f14]) ).
fof(f49,plain,
! [X0] : additive_inverse(X0) = additive_inverse(additive_inverse(multiply(X0,X0))),
inference(forward_demodulation,[],[f46,f16]) ).
fof(f54,plain,
! [X0] : additive_inverse(X0) = multiply(X0,X0),
inference(forward_demodulation,[],[f49,f8]) ).
fof(f56,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[],[f54,f20]) ).
fof(f63,plain,
! [X0] : additive_identity = add(X0,X0),
inference(backward_demodulation,[],[f27,f56]) ).
fof(f64,plain,
~ sP0(additive_identity),
inference(backward_demodulation,[],[f23,f63]) ).
fof(f66,plain,
$false,
inference(forward_subsumption_resolution,[],[f64,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 22:56:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 4.53/1.65 % (1869520)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.53/1.65 % (1869627)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=3759137093:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.53/1.65 % (1869631)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3843310144:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.53/1.65 % (1869626)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=3356532461:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.53/1.65 % (1869629)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=996987861:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.53/1.65 % (1869628)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3447521370:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.53/1.65 % (1869630)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4188892606:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.53/1.65 % (1869629)First to succeed.
% 4.53/1.65 % (1869631)Also succeeded, but the first one will report.
% 4.53/1.65 % (1869630)Also succeeded, but the first one will report.
% 4.53/1.65 % (1869629)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1869520"
% 4.53/1.65 % (1869632)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1904408967:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.53/1.65 % (1869632)Also succeeded, but the first one will report.
% 4.53/1.65 % (1869629)Refutation found. Thanks to Tanya!
% 4.53/1.65 % SZS status Unsatisfiable for theBenchmark
% 4.53/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 4.53/1.65 % (1869629)------------------------------
% 4.53/1.65 % (1869629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.53/1.65 % (1869629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.53/1.65 % (1869629)CaDiCaL version: 2.1.3
% 4.53/1.65 % (1869629)Termination reason: Refutation
% 4.53/1.65 % (1869629)Time elapsed: 0.004 s
% 4.53/1.65 % (1869629)Peak memory usage: 87 MB
% 4.53/1.65 % (1869629)Instructions burned: 2 (million)
% 4.53/1.65 % (1869629)------------------------------
% 4.53/1.65 % (1869629)------------------------------
% 4.53/1.65 % (1869520)Success in time 0.547 s
% 4.53/1.65 % Vampire exiting
%------------------------------------------------------------------------------