%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP571-1 : 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 : n002.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 10:14:53 AM UTC 2026
% Result : Unsatisfiable 2.32s 1.17s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 64 unt; 1 def)
% Number of atoms : 64 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 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 : 106 ( 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
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,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f6,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f7,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,[],[f5,f2,f2,f2,f2]) ).
fof(f8,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(f9,plain,
sP0(double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity)),
inference(inequality_splitting,[],[f7,f8]) ).
fof(f12,plain,
! [X0] : double_divide(double_divide(X0,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = X0,
inference(superposition,[],[f1,f6]) ).
fof(f13,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(X2,identity))) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[],[f1,f1]) ).
fof(f14,plain,
! [X0] : double_divide(double_divide(X0,identity),double_divide(identity,identity)) = X0,
inference(forward_demodulation,[],[f12,f6]) ).
fof(f15,plain,
! [X0] : double_divide(X0,identity) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[],[f1,f14]) ).
fof(f17,plain,
! [X2,X0,X1] : double_divide(X0,identity) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(X2,identity))),
inference(backward_demodulation,[],[f13,f15]) ).
fof(f21,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X0,identity),double_divide(double_divide(X1,X0),double_divide(double_divide(identity,identity),identity))),
inference(superposition,[],[f17,f14]) ).
fof(f24,plain,
! [X0] : double_divide(double_divide(X0,identity),identity) = double_divide(identity,double_divide(X0,double_divide(identity,identity))),
inference(superposition,[],[f17,f14]) ).
fof(f25,plain,
! [X2,X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(double_divide(X0,identity),double_divide(double_divide(X2,identity),identity))),
inference(superposition,[],[f17,f17]) ).
fof(f26,plain,
! [X2,X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(double_divide(X0,identity),double_divide(identity,double_divide(X2,double_divide(identity,identity))))),
inference(backward_demodulation,[],[f25,f24]) ).
fof(f29,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X0,identity),double_divide(double_divide(X1,X0),double_divide(identity,double_divide(identity,double_divide(identity,identity))))),
inference(forward_demodulation,[],[f21,f24]) ).
fof(f32,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X0,identity),double_divide(double_divide(X1,X0),double_divide(identity,identity))),
inference(forward_demodulation,[],[f29,f6]) ).
fof(f41,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(superposition,[],[f15,f6]) ).
fof(f44,plain,
! [X0] : double_divide(double_divide(X0,identity),double_divide(identity,identity)) = double_divide(double_divide(X0,double_divide(identity,identity)),identity),
inference(superposition,[],[f15,f17]) ).
fof(f46,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(double_divide(X1,double_divide(X0,identity)),double_divide(double_divide(identity,identity),identity))),
inference(superposition,[],[f17,f15]) ).
fof(f47,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(double_divide(X1,double_divide(X0,identity)),double_divide(identity,double_divide(identity,double_divide(identity,identity))))),
inference(forward_demodulation,[],[f46,f24]) ).
fof(f49,plain,
! [X0] : double_divide(double_divide(X0,double_divide(identity,identity)),identity) = X0,
inference(forward_demodulation,[],[f44,f14]) ).
fof(f52,plain,
identity = double_divide(identity,identity),
inference(forward_demodulation,[],[f41,f14]) ).
fof(f53,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(double_divide(X1,double_divide(X0,identity)),double_divide(identity,identity))),
inference(forward_demodulation,[],[f47,f6]) ).
fof(f57,plain,
! [X0] : double_divide(double_divide(X0,identity),identity) = double_divide(identity,double_divide(X0,identity)),
inference(backward_demodulation,[],[f24,f52]) ).
fof(f58,plain,
! [X2,X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(double_divide(X0,identity),double_divide(identity,double_divide(X2,identity)))),
inference(backward_demodulation,[],[f26,f52]) ).
fof(f60,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X0,identity),double_divide(double_divide(X1,X0),identity)),
inference(backward_demodulation,[],[f32,f52]) ).
fof(f65,plain,
! [X0] : double_divide(double_divide(X0,identity),identity) = X0,
inference(backward_demodulation,[],[f49,f52]) ).
fof(f67,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(double_divide(identity,double_divide(X0,identity)),double_divide(double_divide(X1,double_divide(X0,identity)),identity)),
inference(forward_demodulation,[],[f53,f52]) ).
fof(f70,plain,
! [X0] : double_divide(identity,double_divide(X0,identity)) = X0,
inference(forward_demodulation,[],[f57,f65]) ).
fof(f71,plain,
! [X2,X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(double_divide(X0,identity),X2)),
inference(backward_demodulation,[],[f58,f70]) ).
fof(f77,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(X0,double_divide(double_divide(X1,double_divide(X0,identity)),identity)),
inference(backward_demodulation,[],[f67,f70]) ).
fof(f83,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(identity,double_divide(double_divide(X1,X0),double_divide(double_divide(X0,identity),identity))),
inference(superposition,[],[f17,f70]) ).
fof(f84,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(identity,double_divide(double_divide(X1,X0),X0)),
inference(forward_demodulation,[],[f83,f65]) ).
fof(f87,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,X0),
inference(superposition,[],[f70,f65]) ).
fof(f121,plain,
! [X0,X1] : double_divide(double_divide(X1,identity),identity) = double_divide(double_divide(X0,X1),double_divide(double_divide(X0,identity),double_divide(identity,identity))),
inference(superposition,[],[f17,f60]) ).
fof(f124,plain,
! [X0,X1] : double_divide(double_divide(X1,identity),identity) = double_divide(double_divide(X0,X1),double_divide(double_divide(X0,identity),identity)),
inference(forward_demodulation,[],[f121,f52]) ).
fof(f131,plain,
! [X0,X1] : double_divide(double_divide(X1,identity),identity) = double_divide(double_divide(X0,X1),X0),
inference(forward_demodulation,[],[f124,f65]) ).
fof(f133,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(forward_demodulation,[],[f131,f65]) ).
fof(f147,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(X0,double_divide(X2,identity))) = double_divide(double_divide(double_divide(X1,X2),X0),identity),
inference(superposition,[],[f17,f133]) ).
fof(f150,plain,
sP0(double_divide(double_divide(c3,b3),double_divide(a3,double_divide(identity,identity)))),
inference(backward_demodulation,[],[f9,f147]) ).
fof(f161,plain,
sP0(double_divide(double_divide(c3,b3),double_divide(a3,identity))),
inference(forward_demodulation,[],[f150,f52]) ).
fof(f170,plain,
~ sP0(double_divide(double_divide(c3,double_divide(identity,double_divide(b3,a3))),identity)),
inference(superposition,[],[f8,f87]) ).
fof(f177,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,identity),identity) = double_divide(double_divide(X2,double_divide(X0,identity)),double_divide(double_divide(X2,identity),double_divide(double_divide(X0,X1),identity))),
inference(superposition,[],[f71,f60]) ).
fof(f182,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,X0),identity) = double_divide(double_divide(X2,X0),double_divide(double_divide(X2,identity),X1)),
inference(superposition,[],[f71,f133]) ).
fof(f191,plain,
! [X2,X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X2,double_divide(X1,double_divide(double_divide(X0,X2),identity))),double_divide(X0,identity)),
inference(superposition,[],[f71,f60]) ).
fof(f205,plain,
! [X2,X0,X1] : double_divide(double_divide(X2,double_divide(X0,identity)),double_divide(double_divide(X2,identity),double_divide(double_divide(X0,X1),identity))) = X1,
inference(forward_demodulation,[],[f177,f65]) ).
fof(f208,plain,
~ sP0(double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3))))),
inference(superposition,[],[f170,f87]) ).
fof(f215,plain,
! [X0,X1] : double_divide(double_divide(X1,X0),identity) = double_divide(identity,double_divide(X0,X1)),
inference(superposition,[],[f84,f133]) ).
fof(f229,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(X0,double_divide(identity,double_divide(double_divide(X0,identity),X1))),
inference(backward_demodulation,[],[f77,f215]) ).
fof(f235,plain,
! [X2,X0,X1] : double_divide(double_divide(X2,double_divide(X0,identity)),double_divide(double_divide(X2,identity),double_divide(identity,double_divide(X1,X0)))) = X1,
inference(backward_demodulation,[],[f205,f215]) ).
fof(f236,plain,
! [X2,X0,X1] : double_divide(identity,double_divide(X0,X1)) = double_divide(double_divide(X2,X0),double_divide(double_divide(X2,identity),X1)),
inference(backward_demodulation,[],[f182,f215]) ).
fof(f237,plain,
! [X2,X0,X1] : double_divide(X1,identity) = double_divide(double_divide(X2,double_divide(X1,double_divide(identity,double_divide(X2,X0)))),double_divide(X0,identity)),
inference(backward_demodulation,[],[f191,f215]) ).
fof(f253,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(X0,identity),double_divide(identity,double_divide(X1,X0)))) = X1,
inference(forward_demodulation,[],[f235,f236]) ).
fof(f353,plain,
! [X0,X1] : double_divide(X1,X0) = double_divide(double_divide(identity,double_divide(X0,X1)),identity),
inference(superposition,[],[f229,f253]) ).
fof(f357,plain,
! [X0,X1] : double_divide(X1,X0) = double_divide(X0,X1),
inference(forward_demodulation,[],[f353,f133]) ).
fof(f787,plain,
sP0(double_divide(double_divide(b3,c3),double_divide(a3,identity))),
inference(superposition,[],[f161,f357]) ).
fof(f809,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,X0),double_divide(X2,identity)) = double_divide(double_divide(double_divide(identity,double_divide(X1,X2)),X0),identity),
inference(superposition,[],[f237,f133]) ).
fof(f845,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,X0),double_divide(X2,identity)) = double_divide(identity,double_divide(X0,double_divide(identity,double_divide(X1,X2)))),
inference(forward_demodulation,[],[f809,f215]) ).
fof(f884,plain,
sP0(double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3))))),
inference(backward_demodulation,[],[f787,f845]) ).
fof(f897,plain,
$false,
inference(forward_subsumption_resolution,[],[f884,f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP571-1 : 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 : n002.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 10:10:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 2.32/1.17 % (3313976)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.32/1.17 % (3314022)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1428411199:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.32/1.17 % (3314022)First to succeed.
% 2.32/1.17 % (3314022)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3313976"
% 2.32/1.17 % (3314019)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=2500688740:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.32/1.17 % (3314020)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=4117878717:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.32/1.17 % (3314023)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1624427065:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.32/1.17 % (3314024)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=918244838:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.32/1.17 % (3314021)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3520279778:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.32/1.17 % (3314025)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=768426175:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.32/1.17 % (3314024)Also succeeded, but the first one will report.
% 2.32/1.17 % (3314023)Instruction limit reached!
% 2.32/1.17 % (3314023)------------------------------
% 2.32/1.17 % (3314023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.17 % (3314023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.17 % (3314023)CaDiCaL version: 2.1.3
% 2.32/1.17 % (3314023)Termination reason: Instruction limit
% 2.32/1.17 % (3314023)Termination phase: Saturation
% 2.32/1.17 % (3314023)Time elapsed: 0.104 s
% 2.32/1.17 % (3314023)Peak memory usage: 89 MB
% 2.32/1.17 % (3314023)Instructions burned: 185 (million)
% 2.32/1.17 % (3314022)Refutation found. Thanks to Tanya!
% 2.32/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.32/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.36 % (3314022)------------------------------
% 2.74/1.36 % (3314022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.36 % (3314022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.36 % (3314022)CaDiCaL version: 2.1.3
% 2.74/1.36 % (3314022)Termination reason: Refutation
% 2.74/1.36 % (3314022)Time elapsed: 0.018 s
% 2.74/1.36 % (3314022)Peak memory usage: 88 MB
% 2.74/1.36 % (3314022)Instructions burned: 51 (million)
% 2.74/1.36 % (3314022)------------------------------
% 2.74/1.36 % (3314022)------------------------------
% 2.74/1.36 % (3313976)Success in time 0.305 s
% 2.74/1.36 % Vampire exiting
%------------------------------------------------------------------------------