%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP609-1 : 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 10:14:58 AM UTC 2026
% Result : Unsatisfiable 3.58s 1.34s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 41 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),X2)),double_divide(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,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,X0,X1] : multiply(double_divide(X0,X2),inverse(double_divide(inverse(double_divide(X0,X1)),X2))) = X1,
inference(forward_demodulation,[],[f1,f2]) ).
fof(f5,plain,
! [X2,X0,X1] : multiply(double_divide(X0,X2),multiply(X2,inverse(double_divide(X0,X1)))) = X1,
inference(forward_demodulation,[],[f4,f2]) ).
fof(f6,plain,
! [X2,X0,X1] : multiply(double_divide(X0,X2),multiply(X2,multiply(X1,X0))) = X1,
inference(forward_demodulation,[],[f5,f2]) ).
fof(f7,plain,
! [X2,X3,X0,X1] : double_divide(X2,X1) = multiply(double_divide(multiply(X1,multiply(X0,X2)),X3),multiply(X3,X0)),
inference(superposition,[],[f6,f6]) ).
fof(f8,plain,
! [X2,X0,X1] : multiply(double_divide(multiply(X0,X1),double_divide(X1,X2)),X0) = X2,
inference(superposition,[],[f6,f6]) ).
fof(f22,plain,
! [X2,X0,X1] : double_divide(X1,multiply(double_divide(multiply(X2,X1),X0),X2)) = X0,
inference(superposition,[],[f7,f8]) ).
fof(f31,plain,
! [X2,X0,X1] : double_divide(multiply(X2,X0),double_divide(X0,multiply(X1,X2))) = X1,
inference(superposition,[],[f22,f7]) ).
fof(f34,plain,
! [X2,X0,X1] : multiply(multiply(double_divide(multiply(X1,X2),X0),X1),X2) = inverse(X0),
inference(superposition,[],[f2,f22]) ).
fof(f45,plain,
! [X2,X0,X1] : inverse(X0) = multiply(double_divide(X1,multiply(X0,X2)),multiply(X2,X1)),
inference(superposition,[],[f2,f31]) ).
fof(f102,plain,
! [X2,X0,X1] : multiply(double_divide(X1,double_divide(X1,multiply(X0,X2))),inverse(X0)) = X2,
inference(superposition,[],[f6,f45]) ).
fof(f127,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(multiply(inverse(X2),X1),multiply(X2,X0)),
inference(superposition,[],[f22,f102]) ).
fof(f159,plain,
! [X2,X0,X1] : multiply(X2,X1) = double_divide(X0,multiply(double_divide(X0,X1),inverse(X2))),
inference(superposition,[],[f22,f127]) ).
fof(f210,plain,
! [X2,X0,X1] : double_divide(X2,X0) = multiply(X1,double_divide(X2,multiply(X1,X0))),
inference(superposition,[],[f159,f102]) ).
fof(f272,plain,
! [X2,X0,X1] : double_divide(X1,X2) = multiply(double_divide(multiply(X2,X1),X0),X0),
inference(superposition,[],[f210,f22]) ).
fof(f300,plain,
! [X2,X3,X0,X1] : double_divide(X1,multiply(double_divide(multiply(X2,X1),X0),X2)) = multiply(double_divide(inverse(X0),X3),X3),
inference(superposition,[],[f272,f34]) ).
fof(f307,plain,
! [X0,X1] : double_divide(X1,double_divide(X1,X0)) = X0,
inference(superposition,[],[f272,f8]) ).
fof(f308,plain,
! [X0,X1] : double_divide(X1,X0) = inverse(multiply(X0,X1)),
inference(superposition,[],[f272,f45]) ).
fof(f310,plain,
! [X0,X1] : inverse(X1) = multiply(double_divide(X0,X1),X0),
inference(superposition,[],[f34,f272]) ).
fof(f338,plain,
! [X3,X0] : multiply(double_divide(inverse(X0),X3),X3) = X0,
inference(forward_demodulation,[],[f300,f22]) ).
fof(f344,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(superposition,[],[f102,f307]) ).
fof(f367,plain,
! [X2,X0,X1] : double_divide(X1,multiply(double_divide(multiply(X2,X1),X0),X2)) = inverse(inverse(X0)),
inference(superposition,[],[f308,f34]) ).
fof(f377,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f367,f22]) ).
fof(f514,plain,
! [X2,X0,X1] : multiply(double_divide(X1,double_divide(X1,inverse(X0))),inverse(double_divide(X2,X0))) = X2,
inference(superposition,[],[f102,f310]) ).
fof(f527,plain,
! [X2,X0,X1] : multiply(double_divide(X1,double_divide(X1,inverse(X0))),multiply(X0,X2)) = X2,
inference(forward_demodulation,[],[f514,f2]) ).
fof(f538,plain,
! [X2,X0] : multiply(inverse(X0),multiply(X0,X2)) = X2,
inference(forward_demodulation,[],[f527,f307]) ).
fof(f550,plain,
! [X0,X1] : multiply(X1,inverse(X1)) = double_divide(inverse(X0),X0),
inference(superposition,[],[f159,f338]) ).
fof(f593,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f344,f344]) ).
fof(f622,plain,
! [X0,X1] : inverse(X1) = multiply(X0,double_divide(X0,X1)),
inference(forward_demodulation,[],[f593,f308]) ).
fof(f757,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,inverse(inverse(X1))),
inference(superposition,[],[f344,f538]) ).
fof(f758,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f757,f377]) ).
fof(f897,plain,
multiply(inverse(a1),a1) != multiply(b1,inverse(b1)),
inference(superposition,[],[f3,f758]) ).
fof(f906,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(forward_demodulation,[],[f897,f758]) ).
fof(f1176,plain,
! [X0,X1] : inverse(inverse(X0)) = double_divide(double_divide(X1,X0),X1),
inference(superposition,[],[f308,f622]) ).
fof(f1183,plain,
! [X0,X1] : double_divide(double_divide(X1,X0),X1) = X0,
inference(forward_demodulation,[],[f1176,f377]) ).
fof(f1200,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[],[f1183,f307]) ).
fof(f3601,plain,
! [X0,X1] : multiply(X1,inverse(X1)) = double_divide(X0,inverse(X0)),
inference(forward_demodulation,[],[f550,f1200]) ).
fof(f3847,plain,
! [X0] : multiply(a1,inverse(a1)) != double_divide(X0,inverse(X0)),
inference(superposition,[],[f906,f3601]) ).
fof(f3916,plain,
$false,
inference(forward_subsumption_resolution,[],[f3847,f3601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP609-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 10:09:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.38 Running first-order theorem proving
% 0.08/0.38 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
% 3.58/1.34 % (2152120)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.58/1.34 % (2152133)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3658902027:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.58/1.34 % (2152133)First to succeed.
% 3.58/1.34 % (2152133)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2152120"
% 3.58/1.34 % (2152129)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=505819993:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.58/1.34 % (2152131)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1364701338:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.58/1.34 % (2152132)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2996958472:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.58/1.34 % (2152130)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=240123525:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.58/1.34 % (2152128)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=907282459:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.58/1.34 % (2152127)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=1528468414:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.58/1.34 % (2152130)Instruction limit reached!
% 3.58/1.34 % (2152130)------------------------------
% 3.58/1.34 % (2152130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.34 % (2152130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.34 % (2152130)CaDiCaL version: 2.1.3
% 3.58/1.34 % (2152130)Termination reason: Instruction limit
% 3.58/1.34 % (2152130)Termination phase: Saturation
% 3.58/1.34 % (2152130)Time elapsed: 0.066 s
% 3.58/1.34 % (2152130)Peak memory usage: 89 MB
% 3.58/1.34 % (2152130)Instructions burned: 138 (million)
% 3.58/1.34 % (2152132)Also succeeded, but the first one will report.
% 3.58/1.34 % (2152131)Instruction limit reached!
% 3.58/1.34 % (2152131)------------------------------
% 3.58/1.34 % (2152131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.34 % (2152131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.34 % (2152131)CaDiCaL version: 2.1.3
% 3.58/1.34 % (2152131)Termination reason: Instruction limit
% 3.58/1.34 % (2152131)Termination phase: Saturation
% 3.58/1.34 % (2152131)Time elapsed: 0.091 s
% 3.58/1.34 % (2152131)Peak memory usage: 90 MB
% 3.58/1.34 % (2152131)Instructions burned: 183 (million)
% 3.58/1.34 % (2152133)Refutation found. Thanks to Tanya!
% 3.58/1.34 % SZS status Unsatisfiable for theBenchmark
% 3.58/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.34 % (2152133)------------------------------
% 3.58/1.34 % (2152133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.34 % (2152133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.34 % (2152133)CaDiCaL version: 2.1.3
% 3.58/1.34 % (2152133)Termination reason: Refutation
% 3.58/1.34 % (2152133)Time elapsed: 0.058 s
% 3.58/1.34 % (2152133)Peak memory usage: 90 MB
% 3.58/1.34 % (2152133)Instructions burned: 171 (million)
% 3.58/1.34 % (2152133)------------------------------
% 3.58/1.34 % (2152133)------------------------------
% 3.58/1.34 % (2152120)Success in time 0.437 s
% 3.58/1.34 % Vampire exiting
%------------------------------------------------------------------------------