%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP509-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 10:17:59 AM UTC 2026
% Result : Unsatisfiable 0.54s 0.52s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 41 ( 41 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 113 ( 113 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f3,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(X0,X3),inverse(multiply(multiply(multiply(X1,X0),X2),X3))),
inference(superposition,[],[f1,f1]) ).
fof(f4,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f5,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(multiply(multiply(X1,X0),X2),X3),inverse(multiply(X1,X2))),inverse(X0)) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f6,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,X2)),inverse(multiply(X0,inverse(multiply(multiply(multiply(X1,X0),X2),X3))))) = X3,
inference(superposition,[],[f4,f1]) ).
fof(f8,plain,
! [X2,X3,X0,X1] : inverse(multiply(X2,X3)) = multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,X0),X3),X1),inverse(X0)))),
inference(superposition,[],[f4,f1]) ).
fof(f11,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X0)))) = multiply(multiply(X0,X3),inverse(multiply(X1,X3))),
inference(superposition,[],[f1,f4]) ).
fof(f22,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(X0,inverse(multiply(X1,X2))),inverse(X0)),
inference(superposition,[],[f3,f1]) ).
fof(f27,plain,
! [X2,X0,X1] : inverse(multiply(X0,multiply(X1,inverse(multiply(multiply(X0,X1),X2))))) = X2,
inference(superposition,[],[f4,f3]) ).
fof(f66,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3)))) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(superposition,[],[f3,f5]) ).
fof(f76,plain,
! [X2,X0] : inverse(X2) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(forward_demodulation,[],[f66,f1]) ).
fof(f81,plain,
! [X3,X0] : multiply(multiply(X3,X0),inverse(X3)) = X0,
inference(superposition,[],[f76,f27]) ).
fof(f82,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(multiply(X1,X0),X2))),
inference(superposition,[],[f76,f1]) ).
fof(f183,plain,
! [X2,X3,X0,X1,X4] : multiply(X0,inverse(multiply(X3,inverse(multiply(multiply(multiply(X1,X3),multiply(X2,inverse(multiply(multiply(X1,X2),X0)))),X4))))) = X4,
inference(superposition,[],[f6,f27]) ).
fof(f222,plain,
! [X2,X3,X0,X1] : inverse(multiply(X3,inverse(multiply(multiply(multiply(X1,X3),X2),X0)))) = multiply(X0,inverse(inverse(multiply(X1,X2)))),
inference(superposition,[],[f81,f6]) ).
fof(f251,plain,
! [X2,X0,X1,X4] : multiply(X0,multiply(X4,inverse(inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(X1,X2),X0)))))))) = X4,
inference(forward_demodulation,[],[f183,f222]) ).
fof(f277,plain,
! [X0,X4] : multiply(X0,multiply(X4,inverse(X0))) = X4,
inference(forward_demodulation,[],[f251,f27]) ).
fof(f290,plain,
! [X2,X0,X1] : multiply(X0,inverse(X1)) = multiply(multiply(X0,X2),inverse(multiply(X1,X2))),
inference(superposition,[],[f1,f277]) ).
fof(f295,plain,
! [X2,X0,X1] : multiply(X1,inverse(multiply(multiply(X2,X1),inverse(X0)))) = multiply(X0,inverse(X2)),
inference(superposition,[],[f4,f277]) ).
fof(f317,plain,
! [X2,X0] : multiply(X0,inverse(X2)) = inverse(multiply(X2,inverse(X0))),
inference(forward_demodulation,[],[f295,f82]) ).
fof(f344,plain,
! [X2,X0,X1] : inverse(multiply(X1,inverse(X1))) = multiply(X2,inverse(multiply(multiply(X0,X2),inverse(X0)))),
inference(superposition,[],[f8,f81]) ).
fof(f359,plain,
! [X2,X0,X1] : inverse(X2) = inverse(multiply(multiply(multiply(X0,X2),X1),inverse(multiply(X0,X1)))),
inference(superposition,[],[f27,f8]) ).
fof(f405,plain,
! [X2,X0,X1] : inverse(X2) = multiply(multiply(X0,X1),inverse(multiply(multiply(X0,X2),X1))),
inference(forward_demodulation,[],[f359,f317]) ).
fof(f417,plain,
! [X0,X1] : inverse(multiply(X1,inverse(X1))) = inverse(multiply(X0,inverse(X0))),
inference(forward_demodulation,[],[f344,f82]) ).
fof(f452,plain,
! [X2,X0] : inverse(X2) = multiply(X0,inverse(multiply(X0,X2))),
inference(forward_demodulation,[],[f405,f290]) ).
fof(f460,plain,
! [X0,X1] : inverse(multiply(X1,inverse(X1))) = multiply(X0,inverse(X0)),
inference(forward_demodulation,[],[f417,f317]) ).
fof(f492,plain,
! [X0,X1] : multiply(X1,inverse(X1)) = multiply(X0,inverse(X0)),
inference(forward_demodulation,[],[f460,f317]) ).
fof(f562,plain,
! [X0,X1] : inverse(inverse(X1)) = multiply(multiply(X1,X0),inverse(X0)),
inference(superposition,[],[f452,f81]) ).
fof(f564,plain,
! [X2,X0,X1] : multiply(X2,X0) = inverse(multiply(X1,inverse(multiply(multiply(X2,X1),X0)))),
inference(superposition,[],[f452,f27]) ).
fof(f568,plain,
! [X0,X1] : multiply(multiply(X1,X0),inverse(X0)) = X1,
inference(superposition,[],[f277,f452]) ).
fof(f616,plain,
! [X2,X0,X1] : multiply(X2,X0) = multiply(multiply(multiply(X2,X1),X0),inverse(X1)),
inference(forward_demodulation,[],[f564,f317]) ).
fof(f617,plain,
! [X1] : inverse(inverse(X1)) = X1,
inference(forward_demodulation,[],[f562,f568]) ).
fof(f1144,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(inverse(multiply(X0,X1)),inverse(multiply(multiply(X2,inverse(multiply(X0,X1))),X3)))) = multiply(multiply(X3,X4),inverse(multiply(inverse(X2),X4))),
inference(superposition,[],[f11,f22]) ).
fof(f1400,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),inverse(multiply(multiply(X2,inverse(multiply(X0,X1))),X3)))) = multiply(X3,inverse(inverse(X2))),
inference(forward_demodulation,[],[f1144,f290]) ).
fof(f1516,plain,
! [X2,X3,X0,X1] : multiply(X3,X2) = inverse(multiply(inverse(multiply(X0,X1)),inverse(multiply(multiply(X2,inverse(multiply(X0,X1))),X3)))),
inference(forward_demodulation,[],[f1400,f617]) ).
fof(f1616,plain,
! [X2,X3,X0,X1] : multiply(X3,X2) = multiply(multiply(multiply(X2,inverse(multiply(X0,X1))),X3),inverse(inverse(multiply(X0,X1)))),
inference(forward_demodulation,[],[f1516,f317]) ).
fof(f1696,plain,
! [X2,X3] : multiply(X2,X3) = multiply(X3,X2),
inference(forward_demodulation,[],[f1616,f616]) ).
fof(f2050,plain,
multiply(inverse(a1),a1) != multiply(b1,inverse(b1)),
inference(superposition,[],[f2,f1696]) ).
fof(f2133,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(forward_demodulation,[],[f2050,f1696]) ).
fof(f2206,plain,
$false,
inference(forward_subsumption_resolution,[],[f2133,f492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP509-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n003.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 10:08:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.42 Running first-order model finding
% 0.15/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.52 % (272662)Will run a generic schedule for satisfiability detection.
% 0.54/0.52 % (272668)% WARNING: option uhcvi not known.
% 0.54/0.52 % (272668)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3700153053:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.54/0.52 % (272671)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2290740770:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.54/0.52 % (272670)dis+10_1_sil=32000:sp=arity:random_seed=2936502074:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.54/0.52 % (272672)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=681168535:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.54/0.52 % (272673)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2997106210:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.54/0.52 % (272667)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3385451617_2999 on theBenchmark for (2999ds/0Mi)
% 0.54/0.52 % TRYING [1]
% 0.54/0.52 % TRYING [2]
% 0.54/0.52 % TRYING [3]
% 0.54/0.52 % (272669)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=630798815:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.54/0.52 % TRYING [4]
% 0.54/0.52 % TRYING [5]
% 0.54/0.52 % (272671) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-272662-272671"...
% 0.54/0.52 % (272671)...printing done.
% 0.54/0.52 % (272671)Refutation found. Thanks to Tanya!
% 0.54/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.54/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.54/0.52 % (272671)------------------------------
% 0.54/0.52 % (272671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.52 % (272671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.52 % (272671)CaDiCaL version: 2.1.3
% 0.54/0.52 % (272671)Termination reason: Refutation
% 0.54/0.52 % (272671)Time elapsed: 0.051 s
% 0.54/0.52 % (272671)Peak memory usage: 12 MB
% 0.54/0.52 % (272671)Instructions burned: 82 (million)
% 0.54/0.52 % (272662)Success in time 0.089 s
% 0.54/0.52 % Vampire exiting
%------------------------------------------------------------------------------