%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG012-6 : 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 : n008.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 12:35:07 PM UTC 2026
% Result : Unsatisfiable 3.08s 1.10s
% Output : Refutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 31 ( 31 unt; 1 def)
% Number of atoms : 31 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_identity) ).
fof(f3,axiom,
! [X0] : multiply(additive_identity,X0) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_zero) ).
fof(f4,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).
fof(f8,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f7]) ).
fof(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f12,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(f13,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] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f20,negated_conjecture,
multiply(additive_inverse(a),additive_inverse(b)) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f21,definition,
~ sP0(multiply(additive_inverse(a),additive_inverse(b))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f22,plain,
sP0(multiply(a,b)),
inference(inequality_splitting,[],[f20,f21]) ).
fof(f50,plain,
! [X0,X1] : add(additive_identity,X1) = add(additive_inverse(X0),add(X0,X1)),
inference(superposition,[],[f15,f8]) ).
fof(f59,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f50,f1]) ).
fof(f68,plain,
! [X0,X1] : add(additive_inverse(X1),add(X0,X1)) = X0,
inference(superposition,[],[f59,f14]) ).
fof(f168,plain,
! [X0,X1] : multiply(X0,additive_identity) = add(multiply(X0,additive_inverse(X1)),multiply(X0,X1)),
inference(superposition,[],[f12,f8]) ).
fof(f189,plain,
! [X0,X1] : additive_identity = add(multiply(X0,additive_inverse(X1)),multiply(X0,X1)),
inference(forward_demodulation,[],[f168,f6]) ).
fof(f286,plain,
! [X0,X1] : multiply(additive_identity,X1) = add(multiply(additive_inverse(X0),X1),multiply(X0,X1)),
inference(superposition,[],[f13,f8]) ).
fof(f303,plain,
! [X0,X1] : additive_identity = add(multiply(additive_inverse(X0),X1),multiply(X0,X1)),
inference(forward_demodulation,[],[f286,f4]) ).
fof(f434,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = add(additive_inverse(multiply(X0,X1)),additive_identity),
inference(superposition,[],[f68,f189]) ).
fof(f435,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(forward_demodulation,[],[f434,f2]) ).
fof(f457,plain,
~ sP0(additive_inverse(multiply(additive_inverse(a),b))),
inference(backward_demodulation,[],[f21,f435]) ).
fof(f503,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = add(additive_inverse(multiply(X0,X1)),additive_identity),
inference(superposition,[],[f68,f303]) ).
fof(f504,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(forward_demodulation,[],[f503,f2]) ).
fof(f525,plain,
~ sP0(additive_inverse(additive_inverse(multiply(a,b)))),
inference(backward_demodulation,[],[f457,f504]) ).
fof(f534,plain,
~ sP0(multiply(a,b)),
inference(forward_demodulation,[],[f525,f11]) ).
fof(f544,plain,
$false,
inference(forward_subsumption_resolution,[],[f534,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG012-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:59:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 3.08/1.10 % (1707916)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.08/1.10 % (1707940)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3257386307:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.08/1.10 % (1707936)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=505331412:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.08/1.10 % (1707935)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=313043934:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.08/1.10 % (1707933)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=1905087387:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.08/1.10 % (1707937)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3531244696:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.08/1.10 % (1707939)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1786797957:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.08/1.10 % (1707934)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=1801991645:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.08/1.10 % (1707937)Refutation not found, incomplete strategy
% 3.08/1.10 % (1707937)------------------------------
% 3.08/1.10 % (1707937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.08/1.10 % (1707937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.08/1.10 % (1707937)CaDiCaL version: 2.1.3
% 3.08/1.10 % (1707937)Termination reason: Refutation not found, incomplete strategy
% 3.08/1.10 % (1707937)Time elapsed: 0.001 s
% 3.08/1.10 % (1707937)Peak memory usage: 87 MB
% 3.08/1.10 % (1707937)Instructions burned: 1 (million)
% 3.08/1.10 % (1707936)First to succeed.
% 3.08/1.10 % (1707936)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1707916"
% 3.08/1.10 % (1707939)Also succeeded, but the first one will report.
% 3.08/1.10 % (1707940)Also succeeded, but the first one will report.
% 3.08/1.10 % (1707937)------------------------------
% 3.08/1.10 % (1707937)------------------------------
% 3.08/1.10 % (1707936)Refutation found. Thanks to Tanya!
% 3.08/1.10 % SZS status Unsatisfiable for theBenchmark
% 3.08/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.08/1.10 % (1707936)------------------------------
% 3.08/1.10 % (1707936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.08/1.10 % (1707936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.08/1.10 % (1707936)CaDiCaL version: 2.1.3
% 3.08/1.10 % (1707936)Termination reason: Refutation
% 3.08/1.10 % (1707936)Time elapsed: 0.013 s
% 3.08/1.10 % (1707936)Peak memory usage: 88 MB
% 3.08/1.10 % (1707936)Instructions burned: 19 (million)
% 3.08/1.10 % (1707936)------------------------------
% 3.08/1.10 % (1707936)------------------------------
% 3.08/1.10 % (1707916)Success in time 0.397 s
% 3.08/1.10 % Vampire exiting
%------------------------------------------------------------------------------