%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP029-1 : 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 : n020.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 10:12:10 AM UTC 2026
% Result : Unsatisfiable 3.56s 1.47s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 44 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 19 |; 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f3,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(f4,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f5,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f6,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f7,negated_conjecture,
! [X0] : ~ product(not_right_identity(X0),X0,not_right_identity(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
fof(f8,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| X0 = X1 ),
inference(resolution,[],[f2,f5]) ).
fof(f9,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| identity = X1 ),
inference(resolution,[],[f2,f6]) ).
fof(f11,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f3,f5]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X0,identity,X3)
| product(X2,X1,X3) ),
inference(resolution,[],[f4,f6]) ).
fof(f27,plain,
! [X2,X0,X1] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f11,f6]) ).
fof(f35,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| identity = X1 ),
inference(resolution,[],[f27,f9]) ).
fof(f44,plain,
! [X0,X1] :
( ~ product(inverse(inverse(X0)),identity,X1)
| product(identity,X0,X1) ),
inference(resolution,[],[f17,f6]) ).
fof(f48,plain,
! [X0,X1] :
( ~ product(X1,inverse(X1),X0)
| identity = X0 ),
inference(resolution,[],[f35,f27]) ).
fof(f55,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(resolution,[],[f48,f1]) ).
fof(f78,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(superposition,[],[f1,f55]) ).
fof(f85,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| product(identity,X0,X1) ),
inference(resolution,[],[f78,f17]) ).
fof(f138,plain,
! [X0] : product(identity,X0,multiply(inverse(inverse(X0)),identity)),
inference(resolution,[],[f44,f1]) ).
fof(f141,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(resolution,[],[f138,f8]) ).
fof(f179,plain,
! [X0] : product(inverse(inverse(X0)),identity,X0),
inference(superposition,[],[f1,f141]) ).
fof(f246,plain,
! [X0] : product(identity,inverse(inverse(X0)),X0),
inference(resolution,[],[f85,f179]) ).
fof(f289,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[],[f246,f8]) ).
fof(f336,plain,
! [X0] : product(X0,identity,X0),
inference(superposition,[],[f179,f289]) ).
fof(f385,plain,
$false,
inference(resolution,[],[f336,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n020.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
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 09:16:19 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 3.56/1.47 % (3120932)Input is clausal, will run a generic CNF schedule.
% 3.56/1.47 % (3120937)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=2182235384:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.56/1.47 % (3120942)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3137403107:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.56/1.47 % (3120938)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3266774417:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.56/1.47 % (3120941)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2781583978:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.56/1.47 % (3120943)dis-21_1_sil=8000:lcm=predicate:random_seed=2589355777: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)
% 3.56/1.47 % (3120940)lrs+10_1_sil=8000:sp=occurrence:random_seed=981493297:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.56/1.47 % (3120939)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2337017193:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.56/1.47 % (3120940)First to succeed.
% 3.56/1.47 % (3120940)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3120932"
% 3.56/1.47 % (3120942)Also succeeded, but the first one will report.
% 3.56/1.47 % (3120943)Also succeeded, but the first one will report.
% 3.56/1.47 % (3120941)Instruction limit reached!
% 3.56/1.47 % (3120941)------------------------------
% 3.56/1.47 % (3120941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (3120941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (3120941)CaDiCaL version: 2.1.3
% 3.56/1.47 % (3120941)Termination reason: Instruction limit
% 3.56/1.47 % (3120941)Termination phase: Saturation
% 3.56/1.47 % (3120941)Time elapsed: 0.061 s
% 3.56/1.47 % (3120941)Peak memory usage: 87 MB
% 3.56/1.47 % (3120941)Instructions burned: 114 (million)
% 3.56/1.47 % (3120951)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=1768278620:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.56/1.47 % (3120951)Refutation not found, incomplete strategy
% 3.56/1.47 % (3120951)------------------------------
% 3.56/1.47 % (3120951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (3120951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (3120951)CaDiCaL version: 2.1.3
% 3.56/1.47 % (3120951)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.47 % (3120951)Time elapsed: 0.001 s
% 3.56/1.47 % (3120951)Peak memory usage: 88 MB
% 3.56/1.47 % (3120940)Refutation found. Thanks to Tanya!
% 3.56/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.56/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.47 % (3120940)------------------------------
% 3.56/1.47 % (3120940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (3120940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (3120940)CaDiCaL version: 2.1.3
% 3.56/1.47 % (3120940)Termination reason: Refutation
% 3.56/1.47 % (3120940)Time elapsed: 0.012 s
% 3.56/1.47 % (3120940)Peak memory usage: 88 MB
% 3.56/1.47 % (3120940)Instructions burned: 15 (million)
% 3.56/1.47 % (3120940)------------------------------
% 3.56/1.47 % (3120940)------------------------------
% 3.56/1.47 % (3120932)Success in time 0.424 s
% 3.56/1.47 % Vampire exiting
%------------------------------------------------------------------------------