%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 10:12:12 AM UTC 2026
% Result : Unsatisfiable 2.60s 1.32s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 10 unt; 1 def)
% Number of atoms : 36 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 15 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f10,axiom,
! [X0] :
( ~ subgroup_member(X0)
| product(another_identity,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_left_identity) ).
fof(f12,axiom,
! [X0] :
( ~ subgroup_member(X0)
| product(X0,another_inverse(X0),another_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_inverse) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f16,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| X1 = X3 ),
inference(reorient_equations,[],[f15]) ).
fof(f19,axiom,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f21,negated_conjecture,
inverse(a) != another_inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).
fof(f22,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( sQ0_eqProxy(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(equality_proxy_replacement,[],[f16,f22]) ).
fof(f25,plain,
~ sQ0_eqProxy(inverse(a),another_inverse(a)),
inference(equality_proxy_replacement,[],[f21,f22]) ).
fof(f29,plain,
product(another_identity,a,a),
inference(resolution,[],[f10,f19]) ).
fof(f37,plain,
product(a,another_inverse(a),another_identity),
inference(resolution,[],[f12,f19]) ).
fof(f43,plain,
! [X0,X1] :
( ~ product(X0,another_inverse(a),X1)
| ~ product(X0,inverse(a),X1) ),
inference(resolution,[],[f23,f25]) ).
fof(f75,plain,
~ product(a,inverse(a),another_identity),
inference(resolution,[],[f37,f43]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ product(X0,inverse(a),X1)
| ~ product(X2,X1,another_identity)
| ~ product(X2,X0,a) ),
inference(resolution,[],[f75,f8]) ).
fof(f99,plain,
! [X0] :
( ~ product(X0,a,a)
| ~ product(X0,identity,another_identity) ),
inference(resolution,[],[f76,f4]) ).
fof(f111,plain,
~ product(another_identity,identity,another_identity),
inference(resolution,[],[f99,f29]) ).
fof(f130,plain,
$false,
inference(resolution,[],[f111,f2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n011.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:15:45 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.60/1.32 % (2139048)Input is clausal, will run a generic CNF schedule.
% 2.60/1.32 % (2139059)dis-21_1_sil=8000:lcm=predicate:random_seed=28964513: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)
% 2.60/1.32 % (2139059)First to succeed.
% 2.60/1.32 % (2139059)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2139048"
% 2.60/1.32 % (2139056)lrs+10_1_sil=8000:sp=occurrence:random_seed=2585097517:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.60/1.32 % (2139058)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=490948894:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.60/1.32 % (2139054)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3892985142:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.60/1.32 % (2139055)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2684774989:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.60/1.32 % (2139053)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=140758301:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.60/1.32 % (2139057)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=941818680:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.60/1.32 % (2139056)Also succeeded, but the first one will report.
% 2.60/1.32 % (2139058)Also succeeded, but the first one will report.
% 2.60/1.32 % (2139057)Also succeeded, but the first one will report.
% 2.60/1.32 % (2139059)Refutation found. Thanks to Tanya!
% 2.60/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.60/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.32 % (2139059)------------------------------
% 2.60/1.32 % (2139059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.32 % (2139059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.32 % (2139059)CaDiCaL version: 2.1.3
% 2.60/1.32 % (2139059)Termination reason: Refutation
% 2.60/1.32 % (2139059)Time elapsed: 0.002 s
% 2.60/1.32 % (2139059)Peak memory usage: 88 MB
% 2.60/1.32 % (2139059)Instructions burned: 3 (million)
% 2.60/1.32 % (2139059)------------------------------
% 2.60/1.32 % (2139059)------------------------------
% 2.60/1.32 % (2139048)Success in time 0.277 s
% 2.60/1.32 % Vampire exiting
%------------------------------------------------------------------------------