%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP412-1 : 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 : n013.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 10:13:56 AM UTC 2026
% Result : Unsatisfiable 4.82s 1.63s
% Output : Refutation 4.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 14 ( 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 : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),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(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X3))),X0))),X3)) = multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X0)),X2))),
inference(superposition,[],[f1,f1]) ).
fof(f18,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(X1))),multiply(multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(multiply(multiply(inverse(X3),X3),inverse(X4))),X0))),X4)))),X1)) = multiply(X2,inverse(multiply(X0,X3))),
inference(superposition,[],[f4,f1]) ).
fof(f22,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(X1))),multiply(inverse(multiply(X2,inverse(X3))),X0)))),X1)) = X0,
inference(superposition,[],[f4,f1]) ).
fof(f24,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1)))) = X2,
inference(superposition,[],[f1,f4]) ).
fof(f54,plain,
! [X0,X1,X5] : inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X5)))),X1)) = X5,
inference(superposition,[],[f22,f22]) ).
fof(f87,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X0)) = multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,X0)),
inference(superposition,[],[f24,f54]) ).
fof(f115,plain,
! [X0,X1,X6,X5] : multiply(inverse(multiply(X1,X0)),multiply(X1,X5)) = multiply(inverse(multiply(X6,X0)),multiply(X6,X5)),
inference(superposition,[],[f87,f22]) ).
fof(f167,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,X1)),multiply(X4,X3)) = multiply(X0,multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,X0)))),X3)),
inference(superposition,[],[f115,f54]) ).
fof(f212,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X2,inverse(multiply(X3,X1)))),multiply(X2,inverse(multiply(multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)),inverse(X4)),multiply(X3,X1))))) = X4,
inference(superposition,[],[f24,f115]) ).
fof(f1695,plain,
! [X2,X3,X0,X1,X4] : multiply(X3,inverse(multiply(multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(multiply(X3,inverse(X4))),inverse(X2)))),X4))) = inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)))),X2)),
inference(superposition,[],[f18,f167]) ).
fof(f1756,plain,
! [X2,X0,X1] : inverse(X2) = inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)))),X2)),
inference(forward_demodulation,[],[f1695,f1]) ).
fof(f1785,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X0),X0))),X1)),
inference(superposition,[],[f1756,f1]) ).
fof(f1929,plain,
! [X2,X0,X1] : multiply(inverse(X2),X2) = multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,inverse(X0))),
inference(superposition,[],[f24,f1785]) ).
fof(f1984,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(multiply(multiply(multiply(inverse(multiply(X4,X3)),multiply(X4,X3)),inverse(X0)),multiply(X2,X3))))) = multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(X5),X5))),X0),
inference(superposition,[],[f212,f1785]) ).
fof(f1986,plain,
! [X0,X5] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(X5),X5))),X0) = X0,
inference(forward_demodulation,[],[f1984,f212]) ).
fof(f2038,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,X0)),multiply(X1,X0)),
inference(superposition,[],[f167,f1986]) ).
fof(f2277,plain,
! [X2,X0] : multiply(inverse(X2),X2) = multiply(inverse(inverse(X0)),inverse(X0)),
inference(forward_demodulation,[],[f1929,f2038]) ).
fof(f2305,plain,
! [X0,X1] : multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f2277,f22]) ).
fof(f3279,plain,
! [X0] : multiply(inverse(a1),a1) != multiply(inverse(X0),X0),
inference(superposition,[],[f2,f2305]) ).
fof(f3352,plain,
$false,
inference(forward_subsumption_resolution,[],[f3279,f2305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP412-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n013.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:02:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 4.82/1.63 % (4169455)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.82/1.63 % (4169465)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2353680265:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.82/1.63 % (4169463)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2429536992:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.82/1.63 % (4169466)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=395509499:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.82/1.63 % (4169460)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=1919329903:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.82/1.63 % (4169462)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=612959023:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.82/1.63 % (4169461)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=1900600617:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.82/1.63 % (4169464)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=445020468:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.82/1.63 % (4169465)Instruction limit reached!
% 4.82/1.63 % (4169465)------------------------------
% 4.82/1.63 % (4169465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.63 % (4169465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.63 % (4169465)CaDiCaL version: 2.1.3
% 4.82/1.63 % (4169465)Termination reason: Instruction limit
% 4.82/1.63 % (4169465)Termination phase: Saturation
% 4.82/1.63 % (4169465)Time elapsed: 0.079 s
% 4.82/1.63 % (4169465)Peak memory usage: 90 MB
% 4.82/1.63 % (4169465)Instructions burned: 260 (million)
% 4.82/1.63 % (4169463)Instruction limit reached!
% 4.82/1.63 % (4169463)------------------------------
% 4.82/1.63 % (4169463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.63 % (4169463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.63 % (4169463)CaDiCaL version: 2.1.3
% 4.82/1.63 % (4169463)Termination reason: Instruction limit
% 4.82/1.63 % (4169463)Termination phase: Saturation
% 4.82/1.63 % (4169463)Time elapsed: 0.075 s
% 4.82/1.63 % (4169463)Peak memory usage: 89 MB
% 4.82/1.63 % (4169463)Instructions burned: 137 (million)
% 4.82/1.63 % (4169464)Instruction limit reached!
% 4.82/1.63 % (4169464)------------------------------
% 4.82/1.63 % (4169464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.63 % (4169464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.63 % (4169464)CaDiCaL version: 2.1.3
% 4.82/1.63 % (4169464)Termination reason: Instruction limit
% 4.82/1.63 % (4169464)Termination phase: Saturation
% 4.82/1.63 % (4169464)Time elapsed: 0.104 s
% 4.82/1.63 % (4169464)Peak memory usage: 89 MB
% 4.82/1.63 % (4169464)Instructions burned: 182 (million)
% 4.82/1.63 % (4169466)First to succeed.
% 4.82/1.63 % (4169466)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4169455"
% 4.82/1.63 % (4169474)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4253580416:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.82/1.63 % (4169475)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4041457591:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.82/1.63 % (4169476)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=664074818:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 4.82/1.63 % (4169476)Instruction limit reached!
% 4.82/1.63 % (4169476)------------------------------
% 4.82/1.63 % (4169476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.63 % (4169476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.63 % (4169476)CaDiCaL version: 2.1.3
% 4.82/1.63 % (4169476)Termination reason: Instruction limit
% 4.82/1.63 % (4169476)Termination phase: Saturation
% 4.82/1.63 % (4169476)Time elapsed: 0.123 s
% 4.82/1.63 % (4169476)Peak memory usage: 89 MB
% 4.82/1.63 % (4169476)Instructions burned: 216 (million)
% 4.82/1.63 % (4169466)Refutation found. Thanks to Tanya!
% 4.82/1.63 % SZS status Unsatisfiable for theBenchmark
% 4.82/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 4.82/1.63 % (4169466)------------------------------
% 4.82/1.63 % (4169466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.63 % (4169466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.63 % (4169466)CaDiCaL version: 2.1.3
% 4.82/1.63 % (4169466)Termination reason: Refutation
% 4.82/1.63 % (4169466)Time elapsed: 0.173 s
% 4.82/1.63 % (4169466)Peak memory usage: 90 MB
% 4.82/1.63 % (4169466)Instructions burned: 321 (million)
% 4.82/1.63 % (4169466)------------------------------
% 4.82/1.63 % (4169466)------------------------------
% 4.82/1.63 % (4169455)Success in time 0.596 s
% 4.82/1.63 % Vampire exiting
%------------------------------------------------------------------------------