%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP048-2 : 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 : n002.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 10:12:14 AM UTC 2026
% Result : Unsatisfiable 5.31s 1.76s
% Output : Refutation 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 17 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 22 ( 22 !; 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(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(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f6,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/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
fof(f8,axiom,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
fof(f9,negated_conjecture,
~ equalish(inverse(a),inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_substitution) ).
fof(f10,plain,
~ product(identity,inverse(b),inverse(a)),
inference(unit_resulting_resolution,[],[f4,f1,f9]) ).
fof(f12,plain,
product(identity,a,b),
inference(unit_resulting_resolution,[],[f7,f1,f8]) ).
fof(f17,plain,
~ product(inverse(inverse(inverse(b))),identity,inverse(a)),
inference(unit_resulting_resolution,[],[f6,f2,f2,f10]) ).
fof(f51,plain,
product(inverse(inverse(a)),identity,b),
inference(unit_resulting_resolution,[],[f5,f2,f2,f12]) ).
fof(f84,plain,
~ product(inverse(inverse(b)),inverse(a),identity),
inference(unit_resulting_resolution,[],[f5,f1,f2,f17]) ).
fof(f92,plain,
~ product(inverse(b),identity,inverse(a)),
inference(unit_resulting_resolution,[],[f5,f1,f2,f84]) ).
fof(f111,plain,
~ product(b,inverse(a),identity),
inference(unit_resulting_resolution,[],[f5,f2,f1,f92]) ).
fof(f127,plain,
~ product(inverse(inverse(a)),identity,b),
inference(unit_resulting_resolution,[],[f6,f2,f1,f111]) ).
fof(f129,plain,
$false,
inference(forward_subsumption_resolution,[],[f127,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.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 09:19:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 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
% 5.31/1.76 % (3269609)Input is clausal, will run a generic CNF schedule.
% 5.31/1.76 % (3269630)dis-21_1_sil=8000:lcm=predicate:random_seed=3474009895: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)
% 5.31/1.76 % (3269630)Instruction limit reached!
% 5.31/1.76 % (3269630)------------------------------
% 5.31/1.76 % (3269630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269630)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269630)Termination reason: Instruction limit
% 5.31/1.76 % (3269630)Termination phase: Saturation
% 5.31/1.76 % (3269630)Time elapsed: 0.036 s
% 5.31/1.76 % (3269630)Peak memory usage: 88 MB
% 5.31/1.76 % (3269630)Instructions burned: 120 (million)
% 5.31/1.76 % (3269624)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=1318104588:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.31/1.76 % (3269628)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3217200223:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.31/1.76 % (3269629)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3671939326:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.31/1.76 % (3269625)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2280483403:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.31/1.76 % (3269626)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3459210433:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.31/1.76 % (3269627)lrs+10_1_sil=8000:sp=occurrence:random_seed=3291979269:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.31/1.76 % (3269628)Instruction limit reached!
% 5.31/1.76 % (3269628)------------------------------
% 5.31/1.76 % (3269628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269628)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269628)Termination reason: Instruction limit
% 5.31/1.76 % (3269628)Termination phase: Saturation
% 5.31/1.76 % (3269628)Time elapsed: 0.064 s
% 5.31/1.76 % (3269628)Peak memory usage: 87 MB
% 5.31/1.76 % (3269628)Instructions burned: 115 (million)
% 5.31/1.76 % (3269629)Instruction limit reached!
% 5.31/1.76 % (3269629)------------------------------
% 5.31/1.76 % (3269629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269629)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269629)Termination reason: Instruction limit
% 5.31/1.76 % (3269629)Termination phase: Saturation
% 5.31/1.76 % (3269629)Time elapsed: 0.103 s
% 5.31/1.76 % (3269629)Peak memory usage: 88 MB
% 5.31/1.76 % (3269629)Instructions burned: 180 (million)
% 5.31/1.76 % (3269637)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=723453546:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.31/1.76 % (3269637)Refutation not found, incomplete strategy
% 5.31/1.76 % (3269637)------------------------------
% 5.31/1.76 % (3269637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269637)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269637)Termination reason: Refutation not found, incomplete strategy
% 5.31/1.76 % (3269637)Time elapsed: 0.0000 s
% 5.31/1.76 % (3269637)Peak memory usage: 87 MB
% 5.31/1.76 % (3269627)Instruction limit reached!
% 5.31/1.76 % (3269627)------------------------------
% 5.31/1.76 % (3269627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269627)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269627)Termination reason: Instruction limit
% 5.31/1.76 % (3269627)Termination phase: Saturation
% 5.31/1.76 % (3269627)Time elapsed: 0.109 s
% 5.31/1.76 % (3269627)Peak memory usage: 88 MB
% 5.31/1.76 % (3269627)Instructions burned: 107 (million)
% 5.31/1.76 % (3269639)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1702101997:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 5.31/1.76 % (3269639)First to succeed.
% 5.31/1.76 % (3269639)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3269609"
% 5.31/1.76 % (3269640)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2216867568:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.31/1.76 % (3269640)Refutation not found, incomplete strategy
% 5.31/1.76 % (3269640)------------------------------
% 5.31/1.76 % (3269640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269640)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269640)Termination reason: Refutation not found, incomplete strategy
% 5.31/1.76 % (3269640)Time elapsed: 0.001 s
% 5.31/1.76 % (3269640)Peak memory usage: 87 MB
% 5.31/1.76 % (3269637)------------------------------
% 5.31/1.76 % (3269637)------------------------------
% 5.31/1.76 % (3269642)lrs+10_64_to=lpo:sil=8000:random_seed=508420425:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.31/1.76 % (3269642)Instruction limit reached!
% 5.31/1.76 % (3269642)------------------------------
% 5.31/1.76 % (3269642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269642)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269642)Termination reason: Instruction limit
% 5.31/1.76 % (3269642)Termination phase: Saturation
% 5.31/1.76 % (3269642)Time elapsed: 0.084 s
% 5.31/1.76 % (3269642)Peak memory usage: 89 MB
% 5.31/1.76 % (3269642)Instructions burned: 127 (million)
% 5.31/1.76 % (3269645)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2796279355:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.31/1.76 % (3269645)Instruction limit reached!
% 5.31/1.76 % (3269645)------------------------------
% 5.31/1.76 % (3269645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269645)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269645)Termination reason: Instruction limit
% 5.31/1.76 % (3269645)Termination phase: Saturation
% 5.31/1.76 % (3269645)Time elapsed: 0.064 s
% 5.31/1.76 % (3269645)Peak memory usage: 89 MB
% 5.31/1.76 % (3269645)Instructions burned: 194 (million)
% 5.31/1.76 % (3269639)Refutation found. Thanks to Tanya!
% 5.31/1.76 % SZS status Unsatisfiable for theBenchmark
% 5.31/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 5.31/1.76 % (3269639)------------------------------
% 5.31/1.76 % (3269639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.76 % (3269639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.76 % (3269639)CaDiCaL version: 2.1.3
% 5.31/1.76 % (3269639)Termination reason: Refutation
% 5.31/1.76 % (3269639)Time elapsed: 0.004 s
% 5.31/1.76 % (3269639)Peak memory usage: 88 MB
% 5.31/1.76 % (3269639)Instructions burned: 5 (million)
% 5.31/1.76 % (3269639)------------------------------
% 5.31/1.76 % (3269639)------------------------------
% 5.31/1.76 % (3269609)Success in time 0.667 s
% 5.31/1.76 % Vampire exiting
%------------------------------------------------------------------------------