%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP012-3 : 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 10:12:06 AM UTC 2026
% Result : Unsatisfiable 4.32s 1.57s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 53 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 27 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity1) ).
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/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f9,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
fof(f12,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[],[f6,f5]) ).
fof(f29,plain,
! [X0] : multiply(identity,X0) = X0,
inference(resolution,[],[f12,f1]) ).
fof(f31,plain,
! [X0] : multiply(X0,identity) = X0,
inference(resolution,[],[f12,f2]) ).
fof(f34,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ product(X5,X0,X3)
| multiply(X5,X2) = X4 ),
inference(resolution,[],[f7,f12]) ).
fof(f41,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X2,X4)
| ~ product(X3,X0,X5)
| multiply(X5,X1) = X4 ),
inference(resolution,[],[f8,f12]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X3,X1,X0)
| multiply(X3,identity) = X2 ),
inference(resolution,[],[f34,f4]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| X2 = X3
| ~ product(X3,X1,X0) ),
inference(forward_demodulation,[],[f111,f31]) ).
fof(f126,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X4)
| ~ product(X0,multiply(X1,X2),X3)
| multiply(X4,X2) = X3 ),
inference(resolution,[],[f41,f5]) ).
fof(f198,plain,
! [X0,X1] :
( ~ product(X1,X0,identity)
| inverse(X0) = X1 ),
inference(resolution,[],[f114,f1]) ).
fof(f199,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,X0)
| multiply(X0,inverse(X1)) = X2 ),
inference(resolution,[],[f114,f5]) ).
fof(f220,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[],[f198,f4]) ).
fof(f266,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(resolution,[],[f199,f5]) ).
fof(f631,plain,
! [X2,X0,X1] :
( ~ product(X0,multiply(inverse(X0),X1),X2)
| multiply(identity,X1) = X2 ),
inference(resolution,[],[f126,f4]) ).
fof(f633,plain,
! [X2,X0,X1] :
( ~ product(X0,multiply(inverse(X0),X1),X2)
| X1 = X2 ),
inference(forward_demodulation,[],[f631,f29]) ).
fof(f637,plain,
! [X0,X1] : multiply(X1,multiply(inverse(X1),X0)) = X0,
inference(resolution,[],[f633,f5]) ).
fof(f649,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[],[f637,f220]) ).
fof(f785,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(superposition,[],[f649,f266]) ).
fof(f1423,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[],[f785,f649]) ).
fof(f3359,plain,
inverse(multiply(a,b)) != inverse(multiply(a,b)),
inference(superposition,[],[f9,f1423]) ).
fof(f3401,plain,
$false,
inference(trivial_inequality_removal,[],[f3359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sun Sep 27 09:14:35 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 4.32/1.57 % (3119205)Input is clausal, will run a generic CNF schedule.
% 4.32/1.57 % (3119211)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=482923048:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.32/1.57 % (3119210)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=4249639315:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.32/1.57 % (3119216)dis-21_1_sil=8000:lcm=predicate:random_seed=1710832770: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)
% 4.32/1.57 % (3119213)lrs+10_1_sil=8000:sp=occurrence:random_seed=3221974707:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.32/1.57 % (3119214)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1022636131:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.32/1.57 % (3119212)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3036554586:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.32/1.57 % (3119215)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2928108829:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.32/1.57 % (3119216)Instruction limit reached!
% 4.32/1.57 % (3119216)------------------------------
% 4.32/1.57 % (3119216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.57 % (3119216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.57 % (3119216)CaDiCaL version: 2.1.3
% 4.32/1.57 % (3119216)Termination reason: Instruction limit
% 4.32/1.57 % (3119216)Termination phase: Saturation
% 4.32/1.57 % (3119216)Time elapsed: 0.067 s
% 4.32/1.57 % (3119216)Peak memory usage: 88 MB
% 4.32/1.57 % (3119216)Instructions burned: 118 (million)
% 4.32/1.57 % (3119213)Instruction limit reached!
% 4.32/1.57 % (3119213)------------------------------
% 4.32/1.57 % (3119213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.57 % (3119213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.57 % (3119213)CaDiCaL version: 2.1.3
% 4.32/1.57 % (3119213)Termination reason: Instruction limit
% 4.32/1.57 % (3119213)Termination phase: Saturation
% 4.32/1.57 % (3119213)Time elapsed: 0.070 s
% 4.32/1.57 % (3119213)Peak memory usage: 87 MB
% 4.32/1.57 % (3119213)Instructions burned: 108 (million)
% 4.32/1.57 % (3119214)Instruction limit reached!
% 4.32/1.57 % (3119214)------------------------------
% 4.32/1.57 % (3119214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.57 % (3119214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.57 % (3119214)CaDiCaL version: 2.1.3
% 4.32/1.57 % (3119214)Termination reason: Instruction limit
% 4.32/1.57 % (3119214)Termination phase: Saturation
% 4.32/1.57 % (3119214)Time elapsed: 0.072 s
% 4.32/1.57 % (3119214)Peak memory usage: 88 MB
% 4.32/1.57 % (3119214)Instructions burned: 116 (million)
% 4.32/1.57 % (3119215)First to succeed.
% 4.32/1.57 % (3119215)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3119205"
% 4.32/1.57 % (3119226)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3357034103:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.32/1.57 % (3119224)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=4284247994:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.32/1.57 % (3119225)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2007223191: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)
% 4.32/1.57 % (3119226)Refutation not found, incomplete strategy
% 4.32/1.57 % (3119226)------------------------------
% 4.32/1.57 % (3119226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.57 % (3119226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.57 % (3119224)Refutation not found, incomplete strategy
% 4.32/1.57 % (3119224)------------------------------
% 4.32/1.57 % (3119224)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.57 % (3119226)CaDiCaL version: 2.1.3
% 4.32/1.57 % (3119226)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.57 % (3119226)Time elapsed: 0.001 s
% 4.32/1.57 % (3119224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.57 % (3119226)Peak memory usage: 87 MB
% 4.32/1.57 % (3119224)CaDiCaL version: 2.1.3
% 4.32/1.57 % (3119224)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.57 % (3119224)Time elapsed: 0.001 s
% 4.32/1.57 % (3119224)Peak memory usage: 87 MB
% 4.32/1.57 % (3119225)Also succeeded, but the first one will report.
% 4.32/1.57 % (3119211)Also succeeded, but the first one will report.
% 4.32/1.57 % (3119215)Refutation found. Thanks to Tanya!
% 4.32/1.57 % SZS status Unsatisfiable for theBenchmark
% 4.32/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 4.32/1.57 % (3119215)------------------------------
% 4.32/1.57 % (3119215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.57 % (3119215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.57 % (3119215)CaDiCaL version: 2.1.3
% 4.32/1.57 % (3119215)Termination reason: Refutation
% 4.32/1.57 % (3119215)Time elapsed: 0.105 s
% 4.32/1.57 % (3119215)Peak memory usage: 89 MB
% 4.32/1.57 % (3119215)Instructions burned: 168 (million)
% 4.32/1.57 % (3119215)------------------------------
% 4.32/1.57 % (3119215)------------------------------
% 4.32/1.57 % (3119205)Success in time 0.537 s
% 4.32/1.57 % Vampire exiting
%------------------------------------------------------------------------------