%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP004-2 : 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 : n016.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 10:12:05 AM UTC 2026
% Result : Unsatisfiable 3.55s 1.22s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 15 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f5,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ product(X2,X3,X0)
| ~ equalish(X0,X1)
| product(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
fof(f8,negated_conjecture,
~ product(a,inverse(a),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_inverse) ).
fof(f10,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| equalish(X1,identity) ),
inference(resolution,[],[f4,f2]) ).
fof(f14,plain,
! [X2,X0,X1] :
( ~ equalish(multiply(X0,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[],[f7,f3]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f5,f1]) ).
fof(f54,plain,
! [X2,X0,X1] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f17,f2]) ).
fof(f116,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X1,identity) ),
inference(resolution,[],[f54,f10]) ).
fof(f131,plain,
! [X0,X1] :
( ~ product(X1,inverse(X1),X0)
| equalish(X0,identity) ),
inference(resolution,[],[f116,f54]) ).
fof(f778,plain,
! [X0] : equalish(multiply(X0,inverse(X0)),identity),
inference(resolution,[],[f131,f3]) ).
fof(f830,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(resolution,[],[f778,f14]) ).
fof(f879,plain,
$false,
inference(resolution,[],[f830,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP004-2 : 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 : n016.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 09:18:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.55/1.22 % (2350873)Input is clausal, will run a generic CNF schedule.
% 3.55/1.22 % (2350960)dis-21_1_sil=8000:lcm=predicate:random_seed=3707115288: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)
% 3.55/1.22 % (2350954)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3684779981:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.55/1.22 % (2350959)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3943166505:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.55/1.22 % (2350955)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2906447330:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.55/1.22 % (2350953)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=3054680856:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.55/1.22 % (2350956)lrs+10_1_sil=8000:sp=occurrence:random_seed=2760164445:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.55/1.22 % (2350960)Instruction limit reached!
% 3.55/1.22 % (2350960)------------------------------
% 3.55/1.22 % (2350960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.22 % (2350960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.22 % (2350960)CaDiCaL version: 2.1.3
% 3.55/1.22 % (2350960)Termination reason: Instruction limit
% 3.55/1.22 % (2350960)Termination phase: Saturation
% 3.55/1.22 % (2350960)Time elapsed: 0.033 s
% 3.55/1.22 % (2350960)Peak memory usage: 88 MB
% 3.55/1.22 % (2350960)Instructions burned: 119 (million)
% 3.55/1.22 % (2350957)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2147346954:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.55/1.22 % (2350956)First to succeed.
% 3.55/1.22 % (2350956)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2350873"
% 3.55/1.22 % (2350959)Also succeeded, but the first one will report.
% 3.55/1.22 % (2350957)Also succeeded, but the first one will report.
% 3.55/1.22 % (2350991)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1513662058:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.55/1.22 % (2350991)Refutation not found, incomplete strategy
% 3.55/1.22 % (2350991)------------------------------
% 3.55/1.22 % (2350991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.22 % (2350991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.22 % (2350991)CaDiCaL version: 2.1.3
% 3.55/1.22 % (2350991)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.22 % (2350991)Time elapsed: 0.001 s
% 3.55/1.22 % (2350991)Peak memory usage: 87 MB
% 3.55/1.22 % (2350991)------------------------------
% 3.55/1.22 % (2350991)------------------------------
% 3.55/1.22 % (2350956)Refutation found. Thanks to Tanya!
% 3.55/1.22 % SZS status Unsatisfiable for theBenchmark
% 3.55/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.22 % (2350956)------------------------------
% 3.55/1.22 % (2350956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.22 % (2350956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.22 % (2350956)CaDiCaL version: 2.1.3
% 3.55/1.22 % (2350956)Termination reason: Refutation
% 3.55/1.22 % (2350956)Time elapsed: 0.027 s
% 3.55/1.22 % (2350956)Peak memory usage: 88 MB
% 3.55/1.22 % (2350956)Instructions burned: 40 (million)
% 3.55/1.22 % (2350956)------------------------------
% 3.55/1.22 % (2350956)------------------------------
% 3.55/1.22 % (2350873)Success in time 0.463 s
% 3.55/1.22 % Vampire exiting
%------------------------------------------------------------------------------