%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG041-1 : 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 : n010.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 12:35:15 PM UTC 2026
% Result : Unsatisfiable 2.70s 1.38s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 23 ( 13 unt; 1 def)
% Number of atoms : 38 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 22 ~; 14 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
fof(f17,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f18,axiom,
! [X0] : product(additive_identity,X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f20,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_identity) ).
fof(f22,axiom,
! [X0] :
( product(X0,h(X0),multiplicative_identity)
| X0 = additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
fof(f23,plain,
! [X0] :
( product(X0,h(X0),multiplicative_identity)
| additive_identity = X0 ),
inference(reorient_equations,[],[f22]) ).
fof(f26,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f27,negated_conjecture,
a != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_additive_identity) ).
fof(f28,plain,
additive_identity != a,
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
fof(f30,plain,
additive_identity != b,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f32,plain,
! [X0] :
( sQ0_eqProxy(additive_identity,X0)
| product(X0,h(X0),multiplicative_identity) ),
inference(equality_proxy_replacement,[],[f23,f31]) ).
fof(f34,plain,
~ sQ0_eqProxy(additive_identity,a),
inference(equality_proxy_replacement,[],[f28,f31]) ).
fof(f35,plain,
~ sQ0_eqProxy(additive_identity,b),
inference(equality_proxy_replacement,[],[f30,f31]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( sQ0_eqProxy(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(equality_proxy_replacement,[],[f17,f31]) ).
fof(f43,plain,
product(b,h(b),multiplicative_identity),
inference(resolution,[],[f32,f35]) ).
fof(f48,plain,
! [X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X0,X1,additive_identity) ),
inference(resolution,[],[f36,f34]) ).
fof(f56,plain,
~ product(a,multiplicative_identity,additive_identity),
inference(resolution,[],[f48,f20]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,multiplicative_identity)
| ~ product(X2,X1,additive_identity)
| ~ product(a,X0,X2) ),
inference(resolution,[],[f56,f10]) ).
fof(f149,plain,
! [X0,X1] :
( ~ product(X1,X0,multiplicative_identity)
| ~ product(a,X1,additive_identity) ),
inference(resolution,[],[f59,f18]) ).
fof(f353,plain,
~ product(a,b,additive_identity),
inference(resolution,[],[f149,f43]) ).
fof(f435,plain,
$false,
inference(resolution,[],[f353,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:02:16 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.70/1.37 % (1405062)Input is clausal, will run a generic CNF schedule.
% 2.70/1.37 % (1405155)dis-21_1_sil=8000:lcm=predicate:random_seed=1199102633:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.70/1.37 % (1405155)First to succeed.
% 2.70/1.37 % (1405155)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1405062"
% 2.70/1.37 % (1405150)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2867376204:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.70/1.37 % (1405148)lrs+10_1_sil=8000:sp=occurrence:random_seed=2006008163:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.70/1.37 % (1405144)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2774468703:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.70/1.37 % (1405147)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2521740775:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.70/1.38 % (1405148)Also succeeded, but the first one will report.
% 2.70/1.38 % (1405154)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=569687570:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.70/1.38 % (1405146)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=712733878:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.70/1.38 % (1405154)Also succeeded, but the first one will report.
% 2.70/1.38 % (1405150)Instruction limit reached!
% 2.70/1.38 % (1405150)------------------------------
% 2.70/1.38 % (1405150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.38 % (1405150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.38 % (1405150)CaDiCaL version: 2.1.3
% 2.70/1.38 % (1405150)Termination reason: Instruction limit
% 2.70/1.38 % (1405150)Termination phase: Saturation
% 2.70/1.38 % (1405150)Time elapsed: 0.071 s
% 2.70/1.38 % (1405150)Peak memory usage: 88 MB
% 2.70/1.38 % (1405150)Instructions burned: 116 (million)
% 2.70/1.38 % (1405155)Refutation found. Thanks to Tanya!
% 2.70/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.70/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.38 % (1405155)------------------------------
% 2.70/1.38 % (1405155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.38 % (1405155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.38 % (1405155)CaDiCaL version: 2.1.3
% 2.70/1.38 % (1405155)Termination reason: Refutation
% 2.70/1.38 % (1405155)Time elapsed: 0.006 s
% 2.70/1.38 % (1405155)Peak memory usage: 88 MB
% 2.70/1.38 % (1405155)Instructions burned: 16 (million)
% 2.70/1.38 % (1405155)------------------------------
% 2.70/1.38 % (1405155)------------------------------
% 2.70/1.38 % (1405062)Success in time 0.325 s
% 2.70/1.38 % Vampire exiting
%------------------------------------------------------------------------------