%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP096-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:12:34 AM UTC 2026
% Result : Unsatisfiable 6.70s 1.91s
% Output : Refutation 6.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 28 unt; 4 def)
% Number of atoms : 78 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 26 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2,f2,f2]) ).
fof(f7,definition,
( spl0_1
<=> divide(a4,inverse(b4)) = divide(b4,inverse(a4)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f11,definition,
( spl0_2
<=> divide(divide(a3,inverse(b3)),inverse(c3)) = divide(a3,inverse(divide(b3,inverse(c3)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| spl0_2 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f15,definition,
( spl0_3
<=> a2 = divide(divide(inverse(b2),inverse(b2)),inverse(a2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f17,plain,
( a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2))
| spl0_3 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f19,definition,
( spl0_4
<=> divide(inverse(a1),inverse(a1)) = divide(inverse(b1),inverse(b1)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f21,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| spl0_4 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f22,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f5,f19,f15,f11,f7]) ).
fof(f23,plain,
! [X2,X3,X0,X1] : divide(divide(divide(X1,inverse(divide(X0,divide(X1,X2)))),inverse(divide(X3,X0))),X2) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f24,plain,
! [X2,X3,X0,X1] : divide(X2,inverse(divide(X0,divide(X2,divide(X1,X3))))) = divide(divide(X1,inverse(X0)),X3),
inference(superposition,[],[f1,f1]) ).
fof(f31,plain,
! [X2,X0] : divide(X0,inverse(divide(X2,X0))) = X2,
inference(superposition,[],[f23,f1]) ).
fof(f37,plain,
! [X2,X0,X1] : divide(X1,inverse(X0)) = divide(X2,inverse(divide(X0,divide(X2,X1)))),
inference(superposition,[],[f31,f1]) ).
fof(f38,plain,
! [X2,X3,X0,X1] : divide(X1,inverse(X0)) = divide(divide(X2,inverse(divide(X3,divide(X2,X1)))),inverse(divide(X0,X3))),
inference(superposition,[],[f31,f23]) ).
fof(f46,plain,
! [X2,X3] : divide(divide(X2,inverse(X3)),X2) = X3,
inference(backward_demodulation,[],[f23,f38]) ).
fof(f50,plain,
! [X3,X0,X1] : divide(divide(X1,inverse(X0)),X3) = divide(divide(X1,X3),inverse(X0)),
inference(backward_demodulation,[],[f24,f37]) ).
fof(f104,plain,
! [X0,X1] : divide(divide(X0,X0),inverse(X1)) = X1,
inference(superposition,[],[f46,f50]) ).
fof(f122,plain,
! [X0,X1] : divide(X0,divide(X1,X1)) = X0,
inference(superposition,[],[f46,f104]) ).
fof(f123,plain,
! [X2,X0,X1] : divide(X0,inverse(X2)) = divide(divide(divide(X1,X1),inverse(X2)),inverse(X0)),
inference(superposition,[],[f50,f104]) ).
fof(f126,plain,
! [X2,X0] : divide(X2,inverse(X0)) = divide(X0,inverse(X2)),
inference(forward_demodulation,[],[f123,f104]) ).
fof(f152,plain,
( divide(b4,inverse(a4)) != divide(b4,inverse(a4))
| spl0_1 ),
inference(superposition,[],[f9,f126]) ).
fof(f153,plain,
! [X2,X0,X1] : divide(divide(X0,inverse(X1)),X2) = divide(divide(X1,X2),inverse(X0)),
inference(superposition,[],[f50,f126]) ).
fof(f154,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X1) = X0,
inference(superposition,[],[f46,f126]) ).
fof(f164,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f152]) ).
fof(f165,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f164]) ).
fof(f170,plain,
! [X0,X1] : divide(divide(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[],[f154,f50]) ).
fof(f182,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(divide(b3,inverse(c3)),inverse(a3))
| spl0_2 ),
inference(forward_demodulation,[],[f13,f126]) ).
fof(f183,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f182,f153]) ).
fof(f184,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f183]) ).
fof(f186,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f17,f104]) ).
fof(f187,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f186]) ).
fof(f201,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(superposition,[],[f46,f170]) ).
fof(f226,plain,
! [X0,X1] : divide(X1,X1) = divide(X0,X0),
inference(superposition,[],[f201,f122]) ).
fof(f258,plain,
( ! [X0] : divide(inverse(a1),inverse(a1)) != divide(X0,X0)
| spl0_4 ),
inference(superposition,[],[f21,f226]) ).
fof(f274,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f258,f226]) ).
fof(f275,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f274]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f165]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f184]) ).
cnf(s5,plain,
spl0_3,
inference(sat_conversion,[],[f187]) ).
cnf(s7,plain,
spl0_4,
inference(sat_conversion,[],[f275]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s5,s4,s3]) ).
fof(f278,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP096-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:18:52 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 5.38/1.72 % (3244691)Input is clausal, will run a generic CNF schedule.
% 5.38/1.72 % (3244729)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3131516107:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.38/1.72 % (3244734)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2741485016:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.38/1.72 % (3244731)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3123673936:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.38/1.72 % (3244732)lrs+10_1_sil=8000:sp=occurrence:random_seed=1612918062:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.38/1.72 % (3244730)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1489815146:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.38/1.72 % (3244733)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1955350761:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.38/1.72 % (3244735)dis-21_1_sil=8000:lcm=predicate:random_seed=1134855507:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 5.38/1.72 % (3244735)Refutation not found, incomplete strategy
% 5.38/1.72 % (3244735)------------------------------
% 5.38/1.72 % (3244735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.72 % (3244735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.72 % (3244735)CaDiCaL version: 2.1.3
% 5.38/1.72 % (3244735)Termination reason: Refutation not found, incomplete strategy
% 5.38/1.72 % (3244735)Time elapsed: 0.001 s
% 5.38/1.72 % (3244735)Peak memory usage: 88 MB
% 5.38/1.72 % (3244732)Instruction limit reached!
% 5.38/1.72 % (3244732)------------------------------
% 5.38/1.72 % (3244732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.72 % (3244732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.72 % (3244732)CaDiCaL version: 2.1.3
% 5.38/1.72 % (3244732)Termination reason: Instruction limit
% 5.38/1.72 % (3244732)Termination phase: Saturation
% 5.38/1.72 % (3244732)Time elapsed: 0.067 s
% 5.38/1.72 % (3244732)Peak memory usage: 90 MB
% 5.38/1.72 % (3244732)Instructions burned: 107 (million)
% 5.38/1.72 % (3244733)Instruction limit reached!
% 5.38/1.72 % (3244733)------------------------------
% 5.38/1.72 % (3244733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.72 % (3244733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.72 % (3244733)CaDiCaL version: 2.1.3
% 5.38/1.72 % (3244733)Termination reason: Instruction limit
% 5.38/1.72 % (3244733)Termination phase: Saturation
% 5.38/1.72 % (3244733)Time elapsed: 0.075 s
% 5.38/1.72 % (3244733)Peak memory usage: 89 MB
% 5.38/1.72 % (3244733)Instructions burned: 117 (million)
% 5.38/1.72 % (3244734)Instruction limit reached!
% 5.38/1.72 % (3244734)------------------------------
% 5.38/1.72 % (3244734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.72 % (3244734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.72 % (3244734)CaDiCaL version: 2.1.3
% 5.38/1.72 % (3244734)Termination reason: Instruction limit
% 5.38/1.72 % (3244734)Termination phase: Saturation
% 5.38/1.72 % (3244734)Time elapsed: 0.104 s
% 5.38/1.72 % (3244734)Peak memory usage: 90 MB
% 5.38/1.72 % (3244734)Instructions burned: 181 (million)
% 5.38/1.72 % (3244743)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1916100732:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.38/1.72 % (3244743)Refutation not found, incomplete strategy
% 5.38/1.72 % (3244743)------------------------------
% 5.38/1.72 % (3244743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.72 % (3244743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.72 % (3244743)CaDiCaL version: 2.1.3
% 5.38/1.72 % (3244743)Termination reason: Refutation not found, incomplete strategy
% 5.38/1.72 % (3244743)Time elapsed: 0.001 s
% 5.38/1.72 % (3244743)Peak memory usage: 88 MB
% 5.38/1.72 % (3244744)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1720622475:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 6.70/1.91 % (3244744)Refutation not found, incomplete strategy
% 6.70/1.91 % (3244744)------------------------------
% 6.70/1.91 % (3244744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/1.91 % (3244744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/1.91 % (3244744)CaDiCaL version: 2.1.3
% 6.70/1.91 % (3244744)Termination reason: Refutation not found, incomplete strategy
% 6.70/1.91 % (3244744)Time elapsed: 0.002 s
% 6.70/1.91 % (3244744)Peak memory usage: 88 MB
% 6.70/1.91 % (3244735)------------------------------
% 6.70/1.91 % (3244735)------------------------------
% 6.70/1.91 % (3244745)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2462340201:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.70/1.91 % (3244745)Refutation not found, incomplete strategy
% 6.70/1.91 % (3244745)------------------------------
% 6.70/1.91 % (3244745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/1.91 % (3244745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/1.91 % (3244745)CaDiCaL version: 2.1.3
% 6.70/1.91 % (3244745)Termination reason: Refutation not found, incomplete strategy
% 6.70/1.91 % (3244745)Time elapsed: 0.001 s
% 6.70/1.91 % (3244745)Peak memory usage: 88 MB
% 6.70/1.91 % (3244749)lrs+10_64_to=lpo:sil=8000:random_seed=371883895:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.70/1.91 % (3244749)First to succeed.
% 6.70/1.91 % (3244749)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3244691"
% 6.70/1.91 % (3244743)------------------------------
% 6.70/1.91 % (3244743)------------------------------
% 6.70/1.91 % (3244729)Also succeeded, but the first one will report.
% 6.70/1.91 % (3244744)------------------------------
% 6.70/1.91 % (3244744)------------------------------
% 6.70/1.91 % (3244745)------------------------------
% 6.70/1.91 % (3244745)------------------------------
% 6.70/1.91 % (3244751)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1568523953:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 6.70/1.91 % (3244751)Also succeeded, but the first one will report.
% 6.70/1.91 % (3244752)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=370622106:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.70/1.91 % (3244730)Also succeeded, but the first one will report.
% 6.70/1.91 % (3244753)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=227133294:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.70/1.91 % (3244749)Refutation found. Thanks to Tanya!
% 6.70/1.91 % SZS status Unsatisfiable for theBenchmark
% 6.70/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 6.70/1.91 % (3244749)------------------------------
% 6.70/1.91 % (3244749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/1.91 % (3244749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/1.91 % (3244749)CaDiCaL version: 2.1.3
% 6.70/1.91 % (3244749)Termination reason: Refutation
% 6.70/1.91 % (3244749)Time elapsed: 0.013 s
% 6.70/1.91 % (3244749)Peak memory usage: 89 MB
% 6.70/1.91 % (3244749)Instructions burned: 17 (million)
% 6.70/1.91 % (3244749)------------------------------
% 6.70/1.91 % (3244749)------------------------------
% 6.70/1.91 % (3244691)Success in time 0.859 s
% 6.70/1.91 % Vampire exiting
%------------------------------------------------------------------------------