%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 10:16:22 AM UTC 2026
% Result : Unsatisfiable 0.48s 0.57s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 37 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
fof(f7,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/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f9,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
fof(f14,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[],[f6,f5]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f7,f1]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( ~ product(X2,X0,X3)
| ~ product(X0,X1,identity)
| product(X3,X1,X2) ),
inference(resolution,[],[f8,f2]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(inverse(X0),X2,X1) ),
inference(resolution,[],[f15,f3]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,identity)
| product(multiply(X2,X0),X1,X2) ),
inference(resolution,[],[f25,f5]) ).
fof(f108,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[],[f58,f5]) ).
fof(f168,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(resolution,[],[f108,f14]) ).
fof(f379,plain,
! [X0,X1] : product(multiply(X0,X1),inverse(X1),X0),
inference(resolution,[],[f93,f4]) ).
fof(f441,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(resolution,[],[f379,f14]) ).
fof(f588,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f441,f168]) ).
fof(f998,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[],[f168,f588]) ).
fof(f1029,plain,
inverse(multiply(a,b)) != inverse(multiply(a,b)),
inference(backward_demodulation,[],[f9,f998]) ).
fof(f1033,plain,
$false,
inference(trivial_inequality_removal,[],[f1029]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:14:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.42 Running first-order model finding
% 0.15/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.57 % (961246)Will run a generic schedule for satisfiability detection.
% 0.48/0.57 % (961254)dis+10_1_sil=32000:sp=arity:random_seed=3145313111:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.48/0.57 % (961252)% WARNING: option uhcvi not known.
% 0.48/0.57 % (961251)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2177516803_2999 on theBenchmark for (2999ds/0Mi)
% 0.48/0.57 % (961252)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2505400959:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.48/0.57 % (961253)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1657767068:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.48/0.57 % (961255)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=933724089:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.48/0.57 % (961256)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4131847402:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.48/0.57 % (961257)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=688810214:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.48/0.57 % TRYING [1]
% 0.48/0.57 % TRYING [2]
% 0.48/0.57 % TRYING [3]
% 0.48/0.57 % TRYING [4]
% 0.48/0.57 % TRYING [5]
% 0.48/0.57 % (961254)Instruction limit reached!
% 0.48/0.57 % (961254)------------------------------
% 0.48/0.57 % (961254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.57 % (961254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.57 % (961254)CaDiCaL version: 2.1.3
% 0.48/0.57 % (961254)Termination reason: Instruction limit
% 0.48/0.57 % (961254)Termination phase: Saturation
% 0.48/0.57 % (961254)Time elapsed: 0.034 s
% 0.48/0.57 % (961254)Peak memory usage: 11 MB
% 0.48/0.57 % (961254)Instructions burned: 103 (million)
% 0.48/0.57 % TRYING [6]
% 0.48/0.57 % (961265)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1273400381:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.48/0.57 % TRYING [1]
% 0.48/0.57 % TRYING [2]
% 0.48/0.57 % TRYING [3]
% 0.48/0.57 % TRYING [4]
% 0.48/0.57 % TRYING [5]
% 0.48/0.57 % (961255)Instruction limit reached!
% 0.48/0.57 % (961255)------------------------------
% 0.48/0.57 % (961255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.57 % (961255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.57 % (961255)CaDiCaL version: 2.1.3
% 0.48/0.57 % (961255)Termination reason: Instruction limit
% 0.48/0.57 % (961255)Termination phase: Saturation
% 0.48/0.57 % (961255)Time elapsed: 0.062 s
% 0.48/0.57 % (961255)Peak memory usage: 11 MB
% 0.48/0.57 % (961255)Instructions burned: 117 (million)
% 0.48/0.57 % TRYING [6]
% 0.48/0.57 % TRYING [7]
% 0.48/0.57 % (961256)Instruction limit reached!
% 0.48/0.57 % (961256)------------------------------
% 0.48/0.57 % (961256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.57 % (961256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.57 % (961256)CaDiCaL version: 2.1.3
% 0.48/0.57 % (961256)Termination reason: Instruction limit
% 0.48/0.57 % (961256)Termination phase: Saturation
% 0.48/0.57 % (961256)Time elapsed: 0.078 s
% 0.48/0.57 % (961256)Peak memory usage: 11 MB
% 0.48/0.57 % (961256)Instructions burned: 131 (million)
% 0.48/0.57 % (961270)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1022174719:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.48/0.57 % (961277)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3406465350:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.48/0.57 % (961257)Instruction limit reached!
% 0.48/0.57 % (961257)------------------------------
% 0.48/0.57 % (961257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.57 % (961257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.57 % (961257)CaDiCaL version: 2.1.3
% 0.48/0.57 % (961257)Termination reason: Instruction limit
% 0.48/0.57 % (961257)Termination phase: Saturation
% 0.48/0.57 % (961257)Time elapsed: 0.106 s
% 0.48/0.57 % (961257)Peak memory usage: 13 MB
% 0.48/0.57 % (961257)Instructions burned: 160 (million)
% 0.48/0.57 % (961270) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-961246-961270"...
% 0.48/0.57 % (961270)...printing done.
% 0.48/0.57 % TRYING [7]
% 0.48/0.57 % (961270)Refutation found. Thanks to Tanya!
% 0.48/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.48/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.48/0.57 % (961270)------------------------------
% 0.48/0.57 % (961270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.57 % (961270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.57 % (961270)CaDiCaL version: 2.1.3
% 0.48/0.57 % (961270)Termination reason: Refutation
% 0.48/0.57 % (961270)Time elapsed: 0.025 s
% 0.48/0.57 % (961270)Peak memory usage: 11 MB
% 0.48/0.57 % (961270)Instructions burned: 33 (million)
% 0.48/0.57 % (961246)Success in time 0.144 s
% 0.48/0.57 % Vampire exiting
%------------------------------------------------------------------------------