%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP406-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 10:13:52 AM UTC 2026
% Result : Unsatisfiable 2.99s 1.03s
% Output : Refutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 11 ( 3 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 : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
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(f4,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X0)),multiply(inverse(X3),multiply(inverse(X3),X3)))) = multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X2),multiply(inverse(X2),X2))))),
inference(superposition,[],[f1,f1]) ).
fof(f20,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X0))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = X0,
inference(superposition,[],[f4,f1]) ).
fof(f22,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X2)),multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(inverse(X2),X2)))))) = X1,
inference(superposition,[],[f1,f4]) ).
fof(f52,plain,
! [X0,X4,X5] : inverse(multiply(inverse(multiply(inverse(multiply(X0,X4)),multiply(X0,X5))),multiply(inverse(X4),multiply(inverse(X4),X4)))) = X5,
inference(superposition,[],[f20,f20]) ).
fof(f94,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,X0)) = multiply(inverse(multiply(X3,X2)),multiply(X3,X0)),
inference(superposition,[],[f22,f52]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X4] : multiply(X0,multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X0))),X3)) = multiply(inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X4,X3)),
inference(superposition,[],[f94,f52]) ).
fof(f140,plain,
! [X2,X3,X0,X1] : multiply(inverse(X2),X1) = multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(X2),X2)))))),
inference(superposition,[],[f22,f94]) ).
fof(f2370,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3))))),multiply(X4,inverse(multiply(inverse(multiply(X0,multiply(inverse(X1),multiply(inverse(X1),X1)))),multiply(X0,multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3))))))))) = X3,
inference(superposition,[],[f22,f114]) ).
fof(f2543,plain,
! [X2,X3,X1] : multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X3,
inference(forward_demodulation,[],[f2370,f140]) ).
fof(f2642,plain,
! [X2,X3,X0] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X3,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X3,multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(superposition,[],[f114,f2543]) ).
fof(f2757,plain,
! [X0,X1] : multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f2642,f2543]) ).
fof(f3251,plain,
! [X0] : multiply(inverse(a1),a1) != multiply(inverse(X0),X0),
inference(superposition,[],[f2,f2757]) ).
fof(f3309,plain,
$false,
inference(forward_subsumption_resolution,[],[f3251,f2757]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP406-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 10:01:50 UTC 2026
% 0.03/0.32 % CPUTime :
% 0.03/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.99/1.03 % (2133204)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.99/1.03 % (2133214)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1437610680:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.99/1.03 % (2133212)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2354412943:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.99/1.03 % (2133215)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2160690951:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.99/1.03 % (2133213)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=620469330:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.99/1.03 % (2133209)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1913790364:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.99/1.03 % (2133210)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3966924985:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.99/1.03 % (2133211)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2705645397:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.99/1.03 % (2133212)Instruction limit reached!
% 2.99/1.03 % (2133212)------------------------------
% 2.99/1.03 % (2133212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.03 % (2133212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.03 % (2133212)CaDiCaL version: 2.1.3
% 2.99/1.03 % (2133212)Termination reason: Instruction limit
% 2.99/1.03 % (2133212)Termination phase: Saturation
% 2.99/1.03 % (2133212)Time elapsed: 0.040 s
% 2.99/1.03 % (2133212)Peak memory usage: 88 MB
% 2.99/1.03 % (2133212)Instructions burned: 138 (million)
% 2.99/1.03 % (2133213)Instruction limit reached!
% 2.99/1.03 % (2133213)------------------------------
% 2.99/1.03 % (2133213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.03 % (2133213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.03 % (2133213)CaDiCaL version: 2.1.3
% 2.99/1.03 % (2133213)Termination reason: Instruction limit
% 2.99/1.03 % (2133213)Termination phase: Saturation
% 2.99/1.03 % (2133213)Time elapsed: 0.052 s
% 2.99/1.03 % (2133213)Peak memory usage: 88 MB
% 2.99/1.03 % (2133213)Instructions burned: 183 (million)
% 2.99/1.03 % (2133214)Instruction limit reached!
% 2.99/1.03 % (2133214)------------------------------
% 2.99/1.03 % (2133214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.03 % (2133214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.03 % (2133214)CaDiCaL version: 2.1.3
% 2.99/1.03 % (2133214)Termination reason: Instruction limit
% 2.99/1.03 % (2133214)Termination phase: Saturation
% 2.99/1.03 % (2133214)Time elapsed: 0.083 s
% 2.99/1.03 % (2133214)Peak memory usage: 90 MB
% 2.99/1.03 % (2133214)Instructions burned: 259 (million)
% 2.99/1.03 % (2133215)First to succeed.
% 2.99/1.03 % (2133215)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2133204"
% 2.99/1.03 % (2133223)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=604380559:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 2.99/1.03 % (2133224)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3102617601:i=4948:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/4948Mi)
% 2.99/1.03 % (2133225)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1601419406:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 2.99/1.03 % (2133215)Refutation found. Thanks to Tanya!
% 2.99/1.03 % SZS status Unsatisfiable for theBenchmark
% 2.99/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 2.99/1.03 % (2133215)------------------------------
% 2.99/1.03 % (2133215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.03 % (2133215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.03 % (2133215)CaDiCaL version: 2.1.3
% 2.99/1.03 % (2133215)Termination reason: Refutation
% 2.99/1.03 % (2133215)Time elapsed: 0.095 s
% 2.99/1.03 % (2133215)Peak memory usage: 90 MB
% 2.99/1.03 % (2133215)Instructions burned: 338 (million)
% 2.99/1.03 % (2133215)------------------------------
% 2.99/1.03 % (2133215)------------------------------
% 2.99/1.03 % (2133204)Success in time 0.387 s
% 2.99/1.03 % Vampire exiting
%------------------------------------------------------------------------------