%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP483-1 : 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 : n019.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 10:14:07 AM UTC 2026
% Result : Unsatisfiable 3.18s 1.35s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 64 unt; 1 def)
% Number of atoms : 64 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),double_divide(X0,identity))),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,plain,
! [X0] : double_divide(X0,identity) = inverse(X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f6,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f7,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f5,f4]) ).
fof(f8,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),
inference(definition_unfolding,[],[f6,f2,f2,f2,f2]) ).
fof(f9,definition,
~ sP0(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f10,plain,
sP0(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity)),
inference(inequality_splitting,[],[f8,f9]) ).
fof(f11,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(double_divide(X2,identity),double_divide(X0,identity))),X1) = X2,
inference(forward_demodulation,[],[f1,f7]) ).
fof(f13,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X0,identity))),X0) = X1,
inference(superposition,[],[f11,f7]) ).
fof(f14,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X3,identity),double_divide(double_divide(double_divide(X1,double_divide(double_divide(X2,identity),identity)),double_divide(double_divide(X0,identity),double_divide(X1,identity))),identity))),X2) = X3,
inference(superposition,[],[f11,f11]) ).
fof(f15,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X3,double_divide(identity,identity)),double_divide(double_divide(X0,identity),double_divide(X3,identity))) = double_divide(double_divide(double_divide(X1,double_divide(X2,identity)),double_divide(X0,double_divide(X1,identity))),X2),
inference(superposition,[],[f11,f11]) ).
fof(f20,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(X0,identity),double_divide(identity,identity))) = double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),X1),
inference(superposition,[],[f13,f13]) ).
fof(f22,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,identity),X0)),double_divide(identity,double_divide(double_divide(X0,identity),double_divide(identity,identity)))) = X1,
inference(superposition,[],[f13,f13]) ).
fof(f23,plain,
! [X0] : double_divide(double_divide(identity,identity),double_divide(X0,identity)) = X0,
inference(superposition,[],[f13,f7]) ).
fof(f24,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(identity,identity))),double_divide(X1,identity)),double_divide(double_divide(X2,identity),X0)),X1) = X2,
inference(superposition,[],[f11,f13]) ).
fof(f25,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(X2,identity)),double_divide(X0,double_divide(X1,identity))),X2) = double_divide(identity,double_divide(double_divide(X0,identity),double_divide(identity,identity))),
inference(superposition,[],[f11,f13]) ).
fof(f27,plain,
! [X0] : identity = double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(identity,identity))),X0),
inference(superposition,[],[f7,f13]) ).
fof(f29,plain,
! [X2] : double_divide(identity,double_divide(double_divide(double_divide(X2,identity),identity),double_divide(identity,identity))) = X2,
inference(backward_demodulation,[],[f11,f25]) ).
fof(f32,plain,
identity = double_divide(identity,identity),
inference(superposition,[],[f7,f23]) ).
fof(f34,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(X2,identity)),double_divide(X0,double_divide(X1,identity))),X2) = double_divide(double_divide(X3,identity),double_divide(double_divide(X0,identity),double_divide(X3,identity))),
inference(backward_demodulation,[],[f15,f32]) ).
fof(f38,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),X1) = double_divide(identity,double_divide(double_divide(X0,identity),identity)),
inference(backward_demodulation,[],[f20,f32]) ).
fof(f40,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,identity),X0)),double_divide(identity,double_divide(double_divide(X0,identity),identity))) = X1,
inference(backward_demodulation,[],[f22,f32]) ).
fof(f41,plain,
! [X0] : double_divide(identity,double_divide(X0,identity)) = X0,
inference(backward_demodulation,[],[f23,f32]) ).
fof(f42,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),double_divide(X1,identity)),double_divide(double_divide(X2,identity),X0)),X1) = X2,
inference(backward_demodulation,[],[f24,f32]) ).
fof(f43,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(X2,identity)),double_divide(X0,double_divide(X1,identity))),X2) = double_divide(identity,double_divide(double_divide(X0,identity),identity)),
inference(backward_demodulation,[],[f25,f32]) ).
fof(f45,plain,
! [X0] : identity = double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),X0),
inference(backward_demodulation,[],[f27,f32]) ).
fof(f46,plain,
! [X2] : double_divide(identity,double_divide(double_divide(double_divide(X2,identity),identity),identity)) = X2,
inference(backward_demodulation,[],[f29,f32]) ).
fof(f47,plain,
! [X2] : double_divide(double_divide(X2,identity),identity) = X2,
inference(backward_demodulation,[],[f46,f41]) ).
fof(f48,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(double_divide(X0,identity),double_divide(X1,identity)),double_divide(double_divide(X2,identity),X0)),X1) = X2,
inference(backward_demodulation,[],[f42,f41]) ).
fof(f49,plain,
! [X2,X0,X1] : double_divide(X0,identity) = double_divide(double_divide(double_divide(X1,double_divide(X2,identity)),double_divide(X0,double_divide(X1,identity))),X2),
inference(backward_demodulation,[],[f43,f41]) ).
fof(f51,plain,
! [X0] : identity = double_divide(double_divide(X0,identity),X0),
inference(backward_demodulation,[],[f45,f41]) ).
fof(f52,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,identity),X0)),double_divide(X0,identity)) = X1,
inference(forward_demodulation,[],[f40,f41]) ).
fof(f53,plain,
! [X0,X1] : double_divide(X0,identity) = double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),X1),
inference(forward_demodulation,[],[f38,f41]) ).
fof(f54,plain,
! [X3,X0] : double_divide(X0,identity) = double_divide(double_divide(X3,identity),double_divide(double_divide(X0,identity),double_divide(X3,identity))),
inference(backward_demodulation,[],[f34,f49]) ).
fof(f55,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X3,identity),double_divide(double_divide(double_divide(X1,X2),double_divide(double_divide(X0,identity),double_divide(X1,identity))),identity))),X2) = X3,
inference(backward_demodulation,[],[f14,f47]) ).
fof(f90,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,X0),
inference(superposition,[],[f41,f47]) ).
fof(f92,plain,
! [X0,X1] : double_divide(double_divide(X1,identity),double_divide(X0,double_divide(X1,identity))) = X0,
inference(superposition,[],[f54,f47]) ).
fof(f102,plain,
! [X2,X3,X0,X1] : double_divide(X0,identity) = double_divide(double_divide(X1,double_divide(X0,double_divide(double_divide(double_divide(X2,X3),double_divide(double_divide(X1,identity),double_divide(X2,identity))),identity))),X3),
inference(superposition,[],[f55,f47]) ).
fof(f123,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(X1,X2),double_divide(double_divide(X0,identity),double_divide(X1,identity))),identity) = double_divide(double_divide(X0,identity),X2),
inference(superposition,[],[f55,f51]) ).
fof(f149,plain,
! [X3,X0,X1] : double_divide(X0,identity) = double_divide(double_divide(X1,double_divide(X0,double_divide(double_divide(X1,identity),X3))),X3),
inference(forward_demodulation,[],[f102,f123]) ).
fof(f176,plain,
sP0(double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),a3))),
inference(superposition,[],[f10,f90]) ).
fof(f177,plain,
~ sP0(double_divide(double_divide(c3,double_divide(identity,double_divide(b3,a3))),identity)),
inference(superposition,[],[f9,f90]) ).
fof(f183,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(superposition,[],[f92,f47]) ).
fof(f190,plain,
sP0(double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3))),
inference(superposition,[],[f176,f90]) ).
fof(f191,plain,
! [X0,X1] : double_divide(X0,identity) = double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X1,identity)),
inference(superposition,[],[f52,f47]) ).
fof(f217,plain,
~ sP0(double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3))))),
inference(superposition,[],[f177,f90]) ).
fof(f308,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,double_divide(X0,double_divide(double_divide(X1,identity),double_divide(X2,identity)))),identity) = double_divide(double_divide(identity,double_divide(X0,identity)),X2),
inference(superposition,[],[f53,f149]) ).
fof(f309,plain,
! [X2,X0,X1] : double_divide(X0,X2) = double_divide(double_divide(X1,double_divide(X0,double_divide(double_divide(X1,identity),double_divide(X2,identity)))),identity),
inference(forward_demodulation,[],[f308,f183]) ).
fof(f365,plain,
! [X0,X1] : double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(X1,identity)),X0),X1) = X0,
inference(superposition,[],[f48,f47]) ).
fof(f393,plain,
! [X0,X1] : double_divide(double_divide(double_divide(identity,double_divide(X1,identity)),X0),X1) = X0,
inference(forward_demodulation,[],[f365,f32]) ).
fof(f432,plain,
! [X0,X1] : double_divide(double_divide(X1,X0),X1) = X0,
inference(forward_demodulation,[],[f393,f183]) ).
fof(f492,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X1,double_divide(X0,double_divide(double_divide(X1,identity),double_divide(X2,identity)))),identity) = double_divide(double_divide(double_divide(X2,double_divide(X3,identity)),double_divide(X0,identity)),X3),
inference(superposition,[],[f49,f149]) ).
fof(f512,plain,
! [X2,X3,X0] : double_divide(X0,X2) = double_divide(double_divide(double_divide(X2,double_divide(X3,identity)),double_divide(X0,identity)),X3),
inference(forward_demodulation,[],[f492,f309]) ).
fof(f1384,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(X0,identity),double_divide(X1,identity)),X2) = double_divide(X1,double_divide(identity,double_divide(X0,X2))),
inference(superposition,[],[f512,f191]) ).
fof(f1397,plain,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),X1) = double_divide(double_divide(double_divide(X1,double_divide(X2,identity)),X0),X2),
inference(superposition,[],[f512,f432]) ).
fof(f1401,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(identity,identity)),double_divide(X0,identity)),X2) = double_divide(double_divide(double_divide(X2,double_divide(X3,identity)),double_divide(X0,X1)),X3),
inference(superposition,[],[f512,f512]) ).
fof(f1459,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X1,identity),double_divide(X0,identity)),X2) = double_divide(double_divide(double_divide(X2,double_divide(X3,identity)),double_divide(X0,X1)),X3),
inference(forward_demodulation,[],[f1401,f32]) ).
fof(f1494,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(X1,identity),double_divide(X0,identity)),X2) = double_divide(double_divide(identity,double_divide(X0,X1)),X2),
inference(forward_demodulation,[],[f1459,f1397]) ).
fof(f1505,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(identity,double_divide(X1,X2))) = double_divide(double_divide(identity,double_divide(X0,X1)),X2),
inference(forward_demodulation,[],[f1494,f1384]) ).
fof(f1516,plain,
sP0(double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3))))),
inference(backward_demodulation,[],[f190,f1505]) ).
fof(f1518,plain,
$false,
inference(forward_subsumption_resolution,[],[f1516,f217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP483-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:05:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.18/1.35 % (2857339)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.18/1.35 % (2857436)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=80374475:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.18/1.35 % (2857431)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=763290313:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.18/1.35 % (2857435)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1399823785:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.18/1.35 % (2857433)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2931869927:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.18/1.35 % (2857434)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2597524551:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.18/1.35 % (2857432)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=2638222337:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.18/1.35 % (2857437)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1379197694:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.18/1.35 % (2857434)First to succeed.
% 3.18/1.35 % (2857434)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2857339"
% 3.18/1.35 % (2857436)Instruction limit reached!
% 3.18/1.35 % (2857436)------------------------------
% 3.18/1.35 % (2857436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.35 % (2857436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.35 % (2857436)CaDiCaL version: 2.1.3
% 3.18/1.35 % (2857436)Termination reason: Instruction limit
% 3.18/1.35 % (2857436)Termination phase: Saturation
% 3.18/1.35 % (2857436)Time elapsed: 0.084 s
% 3.18/1.35 % (2857436)Peak memory usage: 90 MB
% 3.18/1.35 % (2857436)Instructions burned: 259 (million)
% 3.18/1.35 % (2857435)Instruction limit reached!
% 3.18/1.35 % (2857435)------------------------------
% 3.18/1.35 % (2857435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.35 % (2857435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.35 % (2857435)CaDiCaL version: 2.1.3
% 3.18/1.35 % (2857435)Termination reason: Instruction limit
% 3.18/1.35 % (2857435)Termination phase: Saturation
% 3.18/1.35 % (2857435)Time elapsed: 0.093 s
% 3.18/1.35 % (2857435)Peak memory usage: 89 MB
% 3.18/1.35 % (2857435)Instructions burned: 182 (million)
% 3.18/1.35 % (2857437)Also succeeded, but the first one will report.
% 3.18/1.35 % (2857473)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1297063345:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.18/1.35 % (2857474)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2999498:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.18/1.35 % (2857434)Refutation found. Thanks to Tanya!
% 3.18/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.18/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.97/1.46 % (2857434)------------------------------
% 3.97/1.46 % (2857434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.46 % (2857434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.46 % (2857434)CaDiCaL version: 2.1.3
% 3.97/1.46 % (2857434)Termination reason: Refutation
% 3.97/1.46 % (2857434)Time elapsed: 0.049 s
% 3.97/1.46 % (2857434)Peak memory usage: 88 MB
% 3.97/1.46 % (2857434)Instructions burned: 80 (million)
% 3.97/1.46 % (2857434)------------------------------
% 3.97/1.46 % (2857434)------------------------------
% 3.97/1.46 % (2857339)Success in time 0.489 s
% 3.97/1.46 % Vampire exiting
%------------------------------------------------------------------------------