%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP088-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 10:12:33 AM UTC 2026
% Result : Unsatisfiable 4.55s 1.43s
% Output : Refutation 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 46 unt; 4 def)
% Number of atoms : 92 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 23 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 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 : 85 ( 0 sgn 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(X1,divide(X2,divide(X0,X1)))) = X2,
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,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/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f5,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,[],[f4]) ).
fof(f7,definition,
( spl0_1
<=> multiply(a4,b4) = multiply(b4,a4) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( multiply(a4,b4) != multiply(b4,a4)
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f11,definition,
( spl0_2
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f15,definition,
( spl0_3
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f17,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_3 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f19,definition,
( spl0_4
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f21,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),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,X0,X1] : divide(divide(X2,X2),X1) = divide(divide(X0,X0),X1),
inference(superposition,[],[f3,f3]) ).
fof(f29,plain,
! [X0,X1] : divide(X1,inverse(X0)) = multiply(X1,X0),
inference(superposition,[],[f2,f3]) ).
fof(f36,plain,
! [X2,X0,X1] : multiply(X0,divide(X1,divide(X0,divide(X2,X2)))) = X1,
inference(superposition,[],[f1,f2]) ).
fof(f39,plain,
! [X2,X0,X1] : multiply(divide(X0,X0),X1) = inverse(divide(divide(X2,X2),X1)),
inference(superposition,[],[f3,f2]) ).
fof(f46,plain,
! [X0,X1] : inverse(X1) = divide(multiply(inverse(X0),X0),X1),
inference(superposition,[],[f3,f29]) ).
fof(f49,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(superposition,[],[f3,f29]) ).
fof(f139,plain,
! [X2,X3,X0,X1] : divide(X3,X3) = divide(X1,divide(X2,divide(divide(X0,X0),divide(X1,X2)))),
inference(superposition,[],[f1,f23]) ).
fof(f148,plain,
! [X3,X0] : divide(X0,X0) = divide(X3,X3),
inference(forward_demodulation,[],[f139,f1]) ).
fof(f191,plain,
! [X2,X0,X1] : divide(X1,divide(X1,divide(X2,divide(X0,X0)))) = X2,
inference(superposition,[],[f1,f148]) ).
fof(f192,plain,
! [X2,X0,X1] : divide(X1,X2) = divide(X1,divide(X2,divide(X0,X0))),
inference(superposition,[],[f1,f148]) ).
fof(f198,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(backward_demodulation,[],[f36,f192]) ).
fof(f199,plain,
! [X2,X1] : divide(X1,divide(X1,X2)) = X2,
inference(forward_demodulation,[],[f191,f192]) ).
fof(f208,plain,
! [X0,X1] : multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(superposition,[],[f198,f29]) ).
fof(f236,plain,
! [X0,X1] : multiply(divide(X1,X1),X0) = X0,
inference(superposition,[],[f2,f199]) ).
fof(f237,plain,
! [X0,X1] : multiply(divide(X1,X0),X0) = X1,
inference(superposition,[],[f198,f199]) ).
fof(f252,plain,
! [X2,X1] : inverse(divide(divide(X2,X2),X1)) = X1,
inference(backward_demodulation,[],[f39,f236]) ).
fof(f254,plain,
! [X1] : inverse(inverse(X1)) = X1,
inference(backward_demodulation,[],[f49,f236]) ).
fof(f368,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f237,f46]) ).
fof(f383,plain,
! [X2,X0,X1] : inverse(X0) = divide(X2,divide(X0,divide(divide(X1,X1),X2))),
inference(superposition,[],[f252,f1]) ).
fof(f403,plain,
! [X2,X0] : inverse(X0) = divide(X2,multiply(X0,X2)),
inference(forward_demodulation,[],[f383,f2]) ).
fof(f482,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(superposition,[],[f208,f198]) ).
fof(f534,plain,
! [X0,X1] : inverse(inverse(X1)) = divide(multiply(X0,X1),X0),
inference(superposition,[],[f403,f208]) ).
fof(f549,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[],[f237,f403]) ).
fof(f550,plain,
! [X0,X1] : multiply(X0,X1) = divide(X1,inverse(X0)),
inference(superposition,[],[f199,f403]) ).
fof(f567,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[],[f534,f254]) ).
fof(f580,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f237,f567]) ).
fof(f581,plain,
! [X0,X1] : divide(multiply(X1,X0),X0) = X1,
inference(superposition,[],[f199,f567]) ).
fof(f583,plain,
! [X2,X0,X1] : divide(X1,divide(X2,X0)) = multiply(divide(X1,X2),X0),
inference(superposition,[],[f1,f567]) ).
fof(f664,plain,
( multiply(a4,b4) != multiply(a4,b4)
| spl0_1 ),
inference(superposition,[],[f9,f580]) ).
fof(f678,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f664]) ).
fof(f679,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f838,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(superposition,[],[f581,f482]) ).
fof(f1690,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = divide(inverse(X0),X1),
inference(superposition,[],[f838,f550]) ).
fof(f2998,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = divide(X2,divide(inverse(X0),X1)),
inference(superposition,[],[f29,f1690]) ).
fof(f3052,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(divide(X2,inverse(X0)),X1),
inference(forward_demodulation,[],[f2998,f583]) ).
fof(f3083,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(multiply(X2,X0),X1),
inference(forward_demodulation,[],[f3052,f29]) ).
fof(f3176,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(backward_demodulation,[],[f13,f3083]) ).
fof(f3177,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f3176]) ).
fof(f3178,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f3177]) ).
fof(f3251,plain,
( a2 != multiply(inverse(b2),multiply(b2,a2))
| spl0_3 ),
inference(forward_demodulation,[],[f17,f3083]) ).
fof(f3252,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f3251,f549]) ).
fof(f3253,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f3252]) ).
fof(f3255,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f21,f368]) ).
fof(f3256,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f3255]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f679]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f3178]) ).
cnf(s5,plain,
spl0_3,
inference(sat_conversion,[],[f3253]) ).
cnf(s6,plain,
spl0_4,
inference(sat_conversion,[],[f3256]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5,s4,s3]) ).
fof(f3257,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP088-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.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 09:21:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 3.71/1.33 % (3274674)Input is clausal, will run a generic CNF schedule.
% 3.71/1.33 % (3274695)dis-21_1_sil=8000:lcm=predicate:random_seed=3479481906: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)
% 3.71/1.33 % (3274695)Refutation not found, incomplete strategy
% 3.71/1.33 % (3274695)------------------------------
% 3.71/1.33 % (3274695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.33 % (3274695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.33 % (3274695)CaDiCaL version: 2.1.3
% 3.71/1.33 % (3274695)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.33 % (3274695)Time elapsed: 0.001 s
% 3.71/1.33 % (3274695)Peak memory usage: 88 MB
% 3.71/1.33 % (3274691)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=383727680:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.71/1.33 % (3274694)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3442815329:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.71/1.33 % (3274693)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4261575729:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.71/1.33 % (3274690)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2781234447:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.71/1.33 % (3274689)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=3925322476:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.71/1.33 % (3274692)lrs+10_1_sil=8000:sp=occurrence:random_seed=2183043191:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.71/1.33 % (3274693)Instruction limit reached!
% 3.71/1.33 % (3274693)------------------------------
% 3.71/1.33 % (3274693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.33 % (3274693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.33 % (3274693)CaDiCaL version: 2.1.3
% 3.71/1.33 % (3274693)Termination reason: Instruction limit
% 3.71/1.33 % (3274693)Termination phase: Saturation
% 3.71/1.33 % (3274693)Time elapsed: 0.072 s
% 3.71/1.33 % (3274693)Peak memory usage: 89 MB
% 3.71/1.33 % (3274693)Instructions burned: 114 (million)
% 3.71/1.33 % (3274692)Instruction limit reached!
% 3.71/1.33 % (3274692)------------------------------
% 3.71/1.33 % (3274692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.33 % (3274692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.33 % (3274692)CaDiCaL version: 2.1.3
% 3.71/1.33 % (3274692)Termination reason: Instruction limit
% 3.71/1.33 % (3274692)Termination phase: Saturation
% 3.71/1.33 % (3274692)Time elapsed: 0.066 s
% 3.71/1.33 % (3274692)Peak memory usage: 88 MB
% 3.71/1.33 % (3274692)Instructions burned: 107 (million)
% 3.71/1.33 % (3274694)Instruction limit reached!
% 3.71/1.33 % (3274694)------------------------------
% 3.71/1.33 % (3274694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.33 % (3274694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.33 % (3274694)CaDiCaL version: 2.1.3
% 3.71/1.33 % (3274694)Termination reason: Instruction limit
% 3.71/1.33 % (3274694)Termination phase: Saturation
% 3.71/1.33 % (3274694)Time elapsed: 0.102 s
% 3.71/1.33 % (3274694)Peak memory usage: 90 MB
% 3.71/1.33 % (3274694)Instructions burned: 180 (million)
% 3.71/1.33 % (3274695)------------------------------
% 3.71/1.33 % (3274695)------------------------------
% 3.71/1.33 % (3274706)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=1665835430:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.71/1.33 % (3274706)Refutation not found, incomplete strategy
% 3.71/1.33 % (3274706)------------------------------
% 3.71/1.33 % (3274706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.33 % (3274706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.33 % (3274706)CaDiCaL version: 2.1.3
% 3.71/1.33 % (3274706)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.33 % (3274706)Time elapsed: 0.001 s
% 3.71/1.33 % (3274706)Peak memory usage: 88 MB
% 3.71/1.33 % (3274723)lrs+10_64_to=lpo:sil=8000:random_seed=279477067:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.55/1.43 % (3274710)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2566710229: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)
% 4.55/1.43 % (3274710)Refutation not found, incomplete strategy
% 4.55/1.43 % (3274710)------------------------------
% 4.55/1.43 % (3274710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.43 % (3274710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.43 % (3274710)CaDiCaL version: 2.1.3
% 4.55/1.43 % (3274710)Termination reason: Refutation not found, incomplete strategy
% 4.55/1.43 % (3274710)Time elapsed: 0.001 s
% 4.55/1.43 % (3274710)Peak memory usage: 88 MB
% 4.55/1.43 % (3274723)First to succeed.
% 4.55/1.43 % (3274723)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3274674"
% 4.55/1.43 % (3274718)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=141795980:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.55/1.43 % (3274718)Refutation not found, incomplete strategy
% 4.55/1.43 % (3274718)------------------------------
% 4.55/1.43 % (3274718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.43 % (3274718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.43 % (3274718)CaDiCaL version: 2.1.3
% 4.55/1.43 % (3274718)Termination reason: Refutation not found, incomplete strategy
% 4.55/1.43 % (3274718)Time elapsed: 0.001 s
% 4.55/1.43 % (3274718)Peak memory usage: 88 MB
% 4.55/1.43 % (3274723)Refutation found. Thanks to Tanya!
% 4.55/1.43 % SZS status Unsatisfiable for theBenchmark
% 4.55/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 4.55/1.43 % (3274723)------------------------------
% 4.55/1.43 % (3274723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.43 % (3274723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.43 % (3274723)CaDiCaL version: 2.1.3
% 4.55/1.43 % (3274723)Termination reason: Refutation
% 4.55/1.43 % (3274723)Time elapsed: 0.035 s
% 4.55/1.43 % (3274723)Peak memory usage: 90 MB
% 4.55/1.43 % (3274723)Instructions burned: 103 (million)
% 4.55/1.43 % (3274723)------------------------------
% 4.55/1.43 % (3274723)------------------------------
% 4.55/1.43 % (3274674)Success in time 0.585 s
% 4.55/1.43 % Vampire exiting
%------------------------------------------------------------------------------