%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP611-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 10:14:59 AM UTC 2026
% Result : Unsatisfiable 3.12s 1.38s
% Output : Refutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 38 unt; 2 def)
% Number of atoms : 70 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 14 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 107 !; 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/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f5,definition,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f8,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f3,f5]) ).
fof(f9,plain,
( multiply(multiply(a3,b3),c3) != inverse(double_divide(multiply(b3,c3),a3))
| spl0_1 ),
inference(forward_demodulation,[],[f7,f2]) ).
fof(f10,plain,
( multiply(multiply(a3,b3),c3) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| spl0_1 ),
inference(forward_demodulation,[],[f9,f2]) ).
fof(f11,plain,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,multiply(a3,b3)))
| spl0_1 ),
inference(forward_demodulation,[],[f10,f2]) ).
fof(f12,plain,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| spl0_1 ),
inference(forward_demodulation,[],[f11,f2]) ).
fof(f14,definition,
( spl0_2
<=> inverse(double_divide(inverse(double_divide(c3,b3)),a3)) = inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f16,plain,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| spl0_2 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f17,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f12,f5,f14]) ).
fof(f18,plain,
! [X2,X3,X0,X1] : double_divide(X1,X2) = inverse(double_divide(inverse(double_divide(X0,X3)),double_divide(inverse(double_divide(inverse(double_divide(X1,X0)),X2)),X3))),
inference(superposition,[],[f1,f1]) ).
fof(f19,plain,
! [X2,X0,X1] : inverse(double_divide(X0,double_divide(inverse(double_divide(X1,X0)),double_divide(X1,X2)))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f45,plain,
! [X2,X3,X0,X1,X4] : double_divide(X1,X2) = inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X3,X1)),double_divide(X3,X0)),X4)),double_divide(inverse(double_divide(X0,X2)),X4))),
inference(superposition,[],[f18,f19]) ).
fof(f54,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(X1,double_divide(inverse(double_divide(X0,X1)),X2)))) = X2,
inference(superposition,[],[f19,f18]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4] : double_divide(inverse(double_divide(inverse(double_divide(X0,X2)),X1)),X3) = inverse(double_divide(inverse(double_divide(double_divide(X0,X1),X4)),double_divide(inverse(double_divide(X2,X3)),X4))),
inference(superposition,[],[f1,f18]) ).
fof(f65,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X3,double_divide(inverse(double_divide(inverse(double_divide(X1,X2)),X3)),X0))) = double_divide(X1,inverse(double_divide(X2,X0))),
inference(superposition,[],[f54,f54]) ).
fof(f66,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(X0,X1)),double_divide(X0,inverse(double_divide(X1,X2)))) = X2,
inference(superposition,[],[f54,f18]) ).
fof(f81,plain,
! [X2,X3,X0,X1] : inverse(double_divide(inverse(X0),double_divide(X1,inverse(double_divide(X3,double_divide(inverse(double_divide(inverse(double_divide(X1,X2)),X3)),X0)))))) = X2,
inference(superposition,[],[f1,f54]) ).
fof(f87,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(X0),double_divide(X1,double_divide(X1,inverse(double_divide(X2,X0)))))) = X2,
inference(backward_demodulation,[],[f81,f65]) ).
fof(f140,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(inverse(double_divide(X1,inverse(X2))),inverse(double_divide(X0,X2))),
inference(superposition,[],[f54,f87]) ).
fof(f204,plain,
! [X2,X0,X1] : inverse(double_divide(X1,X2)) = double_divide(X0,inverse(double_divide(inverse(X2),double_divide(X0,X1)))),
inference(superposition,[],[f54,f140]) ).
fof(f249,plain,
! [X2,X3,X0,X1] : inverse(double_divide(inverse(double_divide(X1,X2)),X3)) = double_divide(inverse(double_divide(X0,inverse(X2))),inverse(double_divide(inverse(X3),double_divide(X0,X1)))),
inference(superposition,[],[f204,f140]) ).
fof(f251,plain,
! [X2,X0,X1] : double_divide(X2,X0) = inverse(double_divide(X1,double_divide(inverse(double_divide(X2,X0)),X1))),
inference(superposition,[],[f204,f1]) ).
fof(f270,plain,
( ! [X0] : inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(X0,inverse(double_divide(inverse(a3),double_divide(X0,inverse(double_divide(c3,b3))))))
| spl0_2 ),
inference(superposition,[],[f16,f204]) ).
fof(f305,plain,
( ! [X0] : inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(double_divide(X0,inverse(b3))),inverse(double_divide(inverse(a3),double_divide(X0,c3))))
| spl0_2 ),
inference(superposition,[],[f270,f140]) ).
fof(f324,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(inverse(double_divide(X0,X1))),
inference(superposition,[],[f251,f66]) ).
fof(f327,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(superposition,[],[f54,f251]) ).
fof(f328,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(X0,X1)),X2) = inverse(double_divide(inverse(double_divide(double_divide(X0,X1),X3)),double_divide(X2,X3))),
inference(superposition,[],[f1,f251]) ).
fof(f350,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(inverse(double_divide(X0,X2)),X1)),X3) = double_divide(inverse(double_divide(X0,X1)),inverse(double_divide(X2,X3))),
inference(backward_demodulation,[],[f58,f328]) ).
fof(f353,plain,
! [X2,X3,X0,X1] : double_divide(X1,X2) = double_divide(inverse(double_divide(inverse(double_divide(X3,X1)),double_divide(X3,X0))),inverse(double_divide(X0,X2))),
inference(backward_demodulation,[],[f45,f328]) ).
fof(f481,plain,
! [X2,X3,X0,X1] : double_divide(X1,X2) = double_divide(inverse(double_divide(X3,double_divide(X3,X0))),inverse(double_divide(X1,inverse(double_divide(X0,X2))))),
inference(backward_demodulation,[],[f353,f350]) ).
fof(f506,plain,
! [X2,X0,X1] : double_divide(X1,X2) = double_divide(inverse(X0),inverse(double_divide(X1,inverse(double_divide(X0,X2))))),
inference(forward_demodulation,[],[f481,f327]) ).
fof(f569,plain,
! [X2,X0,X1] : inverse(double_divide(X2,X1)) = double_divide(inverse(double_divide(inverse(X2),X0)),double_divide(X0,X1)),
inference(superposition,[],[f66,f506]) ).
fof(f613,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(X1,X2)),X0) = double_divide(X1,inverse(double_divide(X2,X0))),
inference(superposition,[],[f54,f327]) ).
fof(f648,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X1,inverse(double_divide(X2,X3)))) = double_divide(inverse(double_divide(X0,inverse(X2))),inverse(double_divide(inverse(X3),double_divide(X0,X1)))),
inference(backward_demodulation,[],[f249,f613]) ).
fof(f769,plain,
! [X2,X0,X1] : inverse(double_divide(X2,X1)) = double_divide(inverse(X2),inverse(double_divide(X0,double_divide(X0,X1)))),
inference(backward_demodulation,[],[f569,f613]) ).
fof(f810,plain,
( ! [X0] : inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(X0,inverse(double_divide(inverse(b3),inverse(double_divide(inverse(a3),double_divide(X0,c3))))))
| spl0_2 ),
inference(backward_demodulation,[],[f305,f613]) ).
fof(f859,plain,
! [X2,X1] : inverse(double_divide(X2,X1)) = double_divide(inverse(X2),inverse(X1)),
inference(forward_demodulation,[],[f769,f327]) ).
fof(f931,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X1,inverse(double_divide(X2,X3)))) = double_divide(X0,inverse(double_divide(inverse(X2),inverse(double_divide(inverse(X3),double_divide(X0,X1)))))),
inference(forward_demodulation,[],[f648,f613]) ).
fof(f1007,plain,
( ! [X0] : inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(X0,inverse(inverse(double_divide(b3,double_divide(inverse(a3),double_divide(X0,c3))))))
| spl0_2 ),
inference(backward_demodulation,[],[f810,f859]) ).
fof(f1044,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X1,inverse(double_divide(X2,X3)))) = double_divide(X0,inverse(inverse(double_divide(X2,double_divide(inverse(X3),double_divide(X0,X1)))))),
inference(forward_demodulation,[],[f931,f859]) ).
fof(f1070,plain,
( ! [X0] : inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(X0,double_divide(b3,double_divide(inverse(a3),double_divide(X0,c3))))
| spl0_2 ),
inference(forward_demodulation,[],[f1007,f324]) ).
fof(f1095,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X1,inverse(double_divide(X2,X3)))) = double_divide(X0,double_divide(X2,double_divide(inverse(X3),double_divide(X0,X1)))),
inference(forward_demodulation,[],[f1044,f324]) ).
fof(f1136,plain,
( $false
| spl0_2 ),
inference(backward_subsumption_resolution,[],[f1070,f1095]) ).
fof(f1137,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1136]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f8]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f17]) ).
cnf(s6,plain,
spl0_2,
inference(sat_conversion,[],[f1137]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s2,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7]) ).
fof(f1261,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP611-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n001.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 10:15:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.12/1.38 % (3338585)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.12/1.38 % (3338676)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2263445790:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.12/1.38 % (3338670)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=1153132943:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.12/1.38 % (3338673)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=401988070:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.12/1.38 % (3338672)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=1957820947:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.12/1.38 % (3338678)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3077052977:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.12/1.38 % (3338680)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=765619203:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.12/1.38 % (3338674)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=829120949:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.12/1.38 % (3338676)Instruction limit reached!
% 3.12/1.38 % (3338676)------------------------------
% 3.12/1.38 % (3338676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.38 % (3338676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.38 % (3338676)CaDiCaL version: 2.1.3
% 3.12/1.38 % (3338676)Termination reason: Instruction limit
% 3.12/1.38 % (3338676)Termination phase: Saturation
% 3.12/1.38 % (3338676)Time elapsed: 0.058 s
% 3.12/1.38 % (3338676)Peak memory usage: 90 MB
% 3.12/1.38 % (3338676)Instructions burned: 184 (million)
% 3.12/1.38 % (3338674)Instruction limit reached!
% 3.12/1.38 % (3338674)------------------------------
% 3.12/1.38 % (3338674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.38 % (3338674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.38 % (3338674)CaDiCaL version: 2.1.3
% 3.12/1.38 % (3338674)Termination reason: Instruction limit
% 3.12/1.38 % (3338674)Termination phase: Saturation
% 3.12/1.38 % (3338674)Time elapsed: 0.087 s
% 3.12/1.38 % (3338674)Peak memory usage: 89 MB
% 3.12/1.38 % (3338674)Instructions burned: 137 (million)
% 3.12/1.38 % (3338678)First to succeed.
% 3.12/1.38 % (3338678)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3338585"
% 3.12/1.38 % (3338750)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2013771839:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.12/1.38 % (3338759)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3182788967:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.12/1.38 % (3338678)Refutation found. Thanks to Tanya!
% 3.12/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.12/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 4.25/1.48 % (3338678)------------------------------
% 4.25/1.48 % (3338678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.48 % (3338678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.48 % (3338678)CaDiCaL version: 2.1.3
% 4.25/1.48 % (3338678)Termination reason: Refutation
% 4.25/1.48 % (3338678)Time elapsed: 0.115 s
% 4.25/1.48 % (3338678)Peak memory usage: 90 MB
% 4.25/1.48 % (3338678)Instructions burned: 181 (million)
% 4.25/1.48 % (3338678)------------------------------
% 4.25/1.48 % (3338678)------------------------------
% 4.25/1.48 % (3338585)Success in time 0.53 s
% 4.25/1.48 % Vampire exiting
%------------------------------------------------------------------------------