%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP012-2 : 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 : n006.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 10:12:06 AM UTC 2026
% Result : Unsatisfiable 2.77s 1.34s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 46 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f9,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
fof(f10,axiom,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
fof(f11,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_equals_d) ).
fof(f12,plain,
d != inverse(c),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[],[f6,f2]) ).
fof(f16,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| identity = X1 ),
inference(resolution,[],[f6,f3]) ).
fof(f42,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(inverse(X2),X0,X3)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2)
| identity = X4 ),
inference(resolution,[],[f7,f16]) ).
fof(f55,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X2,X3,identity)
| X0 = X1
| ~ product(X4,X3,X1)
| ~ product(X0,X2,X4) ),
inference(resolution,[],[f13,f7]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( ~ product(multiply(inverse(X0),X1),X2,X3)
| ~ product(X1,X2,X0)
| identity = X3 ),
inference(resolution,[],[f42,f5]) ).
fof(f962,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| identity = multiply(multiply(inverse(X2),X0),X1) ),
inference(resolution,[],[f153,f5]) ).
fof(f1034,plain,
! [X2,X3,X0,X1] :
( ~ product(X2,inverse(X3),X1)
| X0 = X1
| ~ product(X0,X3,X2) ),
inference(resolution,[],[f55,f4]) ).
fof(f1113,plain,
identity = multiply(multiply(inverse(c),a),b),
inference(resolution,[],[f962,f9]) ).
fof(f1130,plain,
product(multiply(inverse(c),a),b,identity),
inference(superposition,[],[f5,f1113]) ).
fof(f1796,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| inverse(X1) = X0 ),
inference(resolution,[],[f1034,f1]) ).
fof(f1797,plain,
! [X0] :
( ~ product(X0,a,inverse(b))
| d = X0 ),
inference(resolution,[],[f1034,f10]) ).
fof(f2011,plain,
inverse(b) = multiply(inverse(c),a),
inference(resolution,[],[f1796,f1130]) ).
fof(f2074,plain,
product(inverse(c),a,inverse(b)),
inference(superposition,[],[f5,f2011]) ).
fof(f2091,plain,
d = inverse(c),
inference(resolution,[],[f2074,f1797]) ).
fof(f2115,plain,
$false,
inference(forward_subsumption_resolution,[],[f2091,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.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 09:13:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.77/1.34 % (2720119)Input is clausal, will run a generic CNF schedule.
% 2.77/1.34 % (2720250)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1214756497:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.34 % (2720246)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3833053157:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.34 % (2720247)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1952637209:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.34 % (2720248)lrs+10_1_sil=8000:sp=occurrence:random_seed=288475018:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.34 % (2720245)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=903455751:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.34 % (2720251)dis-21_1_sil=8000:lcm=predicate:random_seed=272306289: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)
% 2.77/1.34 % (2720250)First to succeed.
% 2.77/1.34 % (2720250)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2720119"
% 2.77/1.34 % (2720249)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2720936419:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.34 % (2720248)Also succeeded, but the first one will report.
% 2.77/1.34 % (2720251)Instruction limit reached!
% 2.77/1.34 % (2720251)------------------------------
% 2.77/1.34 % (2720251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.34 % (2720251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.34 % (2720251)CaDiCaL version: 2.1.3
% 2.77/1.34 % (2720251)Termination reason: Instruction limit
% 2.77/1.34 % (2720251)Termination phase: Saturation
% 2.77/1.34 % (2720251)Time elapsed: 0.067 s
% 2.77/1.34 % (2720251)Peak memory usage: 88 MB
% 2.77/1.34 % (2720251)Instructions burned: 118 (million)
% 2.77/1.34 % (2720249)Instruction limit reached!
% 2.77/1.34 % (2720249)------------------------------
% 2.77/1.34 % (2720249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.34 % (2720249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.34 % (2720249)CaDiCaL version: 2.1.3
% 2.77/1.34 % (2720249)Termination reason: Instruction limit
% 2.77/1.34 % (2720249)Termination phase: Saturation
% 2.77/1.34 % (2720249)Time elapsed: 0.075 s
% 2.77/1.34 % (2720249)Peak memory usage: 88 MB
% 2.77/1.34 % (2720249)Instructions burned: 114 (million)
% 2.77/1.34 % (2720250)Refutation found. Thanks to Tanya!
% 2.77/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.34 % (2720250)------------------------------
% 2.77/1.34 % (2720250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.34 % (2720250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.34 % (2720250)CaDiCaL version: 2.1.3
% 2.77/1.34 % (2720250)Termination reason: Refutation
% 2.77/1.34 % (2720250)Time elapsed: 0.044 s
% 2.77/1.34 % (2720250)Peak memory usage: 89 MB
% 2.77/1.34 % (2720250)Instructions burned: 119 (million)
% 2.77/1.34 % (2720250)------------------------------
% 2.77/1.34 % (2720250)------------------------------
% 2.77/1.34 % (2720119)Success in time 0.302 s
% 2.77/1.34 % Vampire exiting
%------------------------------------------------------------------------------