%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP449-1 : 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 : n007.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 10:14:02 AM UTC 2026
% Result : Unsatisfiable 3.69s 1.49s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 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 : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(divide(divide(divide(X1,X1),X1),X2),divide(divide(divide(X1,X1),X0),X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,plain,
! [X0,X1] : divide(divide(X1,X1),X0) = inverse(X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f6,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
! [X0,X1] : inverse(X1) = divide(inverse(divide(X0,X0)),X1),
inference(superposition,[],[f4,f4]) ).
fof(f16,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f2,f4]) ).
fof(f17,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(divide(X1,X1),X0),
inference(superposition,[],[f16,f4]) ).
fof(f29,plain,
! [X0,X1] : inverse(inverse(X1)) = multiply(multiply(inverse(X0),X0),X1),
inference(superposition,[],[f17,f16]) ).
fof(f36,plain,
! [X2,X0,X1] : divide(X0,divide(divide(divide(divide(X1,X1),X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[],[f1,f4]) ).
fof(f37,plain,
! [X2,X0,X1] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[],[f36,f4]) ).
fof(f53,plain,
a2 != inverse(inverse(a2)),
inference(superposition,[],[f6,f29]) ).
fof(f64,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(superposition,[],[f37,f4]) ).
fof(f70,plain,
! [X2,X0,X1] : inverse(divide(divide(inverse(X0),X2),divide(inverse(divide(X1,X1)),X2))) = X0,
inference(superposition,[],[f4,f37]) ).
fof(f77,plain,
! [X2,X0] : inverse(divide(divide(inverse(X0),X2),inverse(X2))) = X0,
inference(forward_demodulation,[],[f70,f7]) ).
fof(f81,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[],[f64,f16]) ).
fof(f89,plain,
! [X2,X0] : inverse(multiply(divide(inverse(X0),X2),X2)) = X0,
inference(forward_demodulation,[],[f77,f16]) ).
fof(f93,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f81,f16]) ).
fof(f98,plain,
! [X0,X1] : multiply(inverse(inverse(X1)),X0) = multiply(X1,X0),
inference(superposition,[],[f93,f93]) ).
fof(f117,plain,
! [X0,X1] : divide(X1,X1) = inverse(multiply(inverse(X0),X0)),
inference(superposition,[],[f89,f7]) ).
fof(f205,plain,
! [X0,X1] : divide(X1,X1) = divide(X0,X0),
inference(superposition,[],[f117,f117]) ).
fof(f288,plain,
! [X0,X1] : divide(X1,divide(X0,X0)) = X1,
inference(superposition,[],[f37,f205]) ).
fof(f328,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,X0))) = X1,
inference(superposition,[],[f288,f4]) ).
fof(f367,plain,
! [X0,X1] : multiply(X1,divide(X0,X0)) = X1,
inference(forward_demodulation,[],[f328,f16]) ).
fof(f397,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(X0,divide(X1,X1)),
inference(superposition,[],[f98,f367]) ).
fof(f398,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f397,f367]) ).
fof(f413,plain,
a2 != a2,
inference(superposition,[],[f53,f398]) ).
fof(f427,plain,
$false,
inference(trivial_inequality_removal,[],[f413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP449-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.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 10:02:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.69/1.49 % (1172718)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.69/1.49 % (1172726)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1358350025:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.69/1.49 % (1172725)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2332148931:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.69/1.49 % (1172723)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=2702907478:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.69/1.49 % (1172724)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=692136589:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.69/1.49 % (1172727)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3008237484:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.69/1.49 % (1172728)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=87557391:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.69/1.49 % (1172729)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3112952703:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.69/1.49 % (1172726)Instruction limit reached!
% 3.69/1.49 % (1172726)------------------------------
% 3.69/1.49 % (1172726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.49 % (1172726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.49 % (1172726)CaDiCaL version: 2.1.3
% 3.69/1.49 % (1172726)Termination reason: Instruction limit
% 3.69/1.49 % (1172726)Termination phase: Saturation
% 3.69/1.49 % (1172726)Time elapsed: 0.045 s
% 3.69/1.49 % (1172726)Peak memory usage: 89 MB
% 3.69/1.49 % (1172726)Instructions burned: 139 (million)
% 3.69/1.49 % (1172729)First to succeed.
% 3.69/1.49 % (1172729)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1172718"
% 3.69/1.49 % (1172728)Also succeeded, but the first one will report.
% 3.69/1.49 % (1172727)Also succeeded, but the first one will report.
% 3.69/1.49 % (1172737)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=513474331:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.69/1.49 % (1172729)Refutation found. Thanks to Tanya!
% 3.69/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.69/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.49 % (1172729)------------------------------
% 3.69/1.49 % (1172729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.49 % (1172729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.49 % (1172729)CaDiCaL version: 2.1.3
% 3.69/1.49 % (1172729)Termination reason: Refutation
% 3.69/1.49 % (1172729)Time elapsed: 0.010 s
% 3.69/1.49 % (1172729)Peak memory usage: 88 MB
% 3.69/1.49 % (1172729)Instructions burned: 15 (million)
% 3.69/1.49 % (1172729)------------------------------
% 3.69/1.49 % (1172729)------------------------------
% 3.69/1.49 % (1172718)Success in time 0.449 s
% 3.69/1.49 % Vampire exiting
%------------------------------------------------------------------------------