%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:13:02 AM UTC 2026
% Result : Unsatisfiable 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 76 ( 11 unt; 7 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 195 ( 92 ~; 96 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f5,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f7,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f8,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f12,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X0,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_1) ).
fof(f13,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_2) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_1,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_2)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f6,f13]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(X2,e_1,X3)
| ~ product(X2,e_2,X0)
| ~ product(e_1,X3,X1) ),
inference(resolution,[],[f6,f12]) ).
fof(f16,plain,
! [X0] :
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) ),
inference(factoring,[],[f14]) ).
fof(f19,definition,
( spl0_1
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f20,plain,
( product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f21,plain,
( ~ product(e_1,e_2,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f27,definition,
( spl0_3
<=> ! [X0] :
( ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f28,plain,
( ! [X0] :
( ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f30,definition,
( spl0_4
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f32,plain,
( ~ product(e_1,e_1,e_1)
| spl0_4 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f33,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f16,f30,f27]) ).
fof(f43,definition,
( spl0_6
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f44,plain,
( product(e_2,e_2,e_2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f48,definition,
( spl0_7
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f57,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2) ),
inference(resolution,[],[f8,f4]) ).
fof(f58,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,X0,e_1)
| product(X0,X0,e_2) ),
inference(factoring,[],[f8]) ).
fof(f59,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2) ),
inference(resolution,[],[f5,f8]) ).
fof(f60,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[],[f58,f4]) ).
fof(f63,plain,
( product(e_1,e_1,e_2)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f60,f32]) ).
fof(f67,plain,
( ! [X0,X1] :
( ~ product(e_1,X1,e_2)
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_1,X1) )
| ~ spl0_6 ),
inference(resolution,[],[f44,f15]) ).
fof(f73,plain,
( ! [X0] :
( equalish(e_1,X0)
| ~ product(X0,e_1,e_2) )
| spl0_4 ),
inference(resolution,[],[f63,f11]) ).
fof(f74,plain,
( ! [X0] :
( equalish(e_1,X0)
| ~ product(e_1,X0,e_2) )
| spl0_4 ),
inference(resolution,[],[f63,f10]) ).
fof(f78,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[],[f57,f5]) ).
fof(f79,plain,
( product(e_1,e_2,e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f78,f21]) ).
fof(f80,plain,
( ! [X0] :
( equalish(e_1,X0)
| ~ product(X0,e_2,e_1) )
| spl0_1 ),
inference(resolution,[],[f79,f11]) ).
fof(f81,plain,
( ! [X0] :
( equalish(e_2,X0)
| ~ product(e_1,X0,e_1) )
| spl0_1 ),
inference(resolution,[],[f79,f10]) ).
fof(f83,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[],[f59,f4]) ).
fof(f84,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[],[f59,f5]) ).
fof(f86,definition,
( spl0_9
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,definition,
( spl0_10
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f92,plain,
( product(e_2,e_1,e_1)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f83,f90,f86]) ).
fof(f98,plain,
( ~ product(e_2,e_1,e_2)
| spl0_4 ),
inference(resolution,[],[f73,f6]) ).
fof(f99,plain,
( ~ spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f98,f30,f86]) ).
fof(f100,plain,
( ~ product(e_1,e_2,e_2)
| spl0_4 ),
inference(resolution,[],[f74,f6]) ).
fof(f102,plain,
( ~ product(e_2,e_2,e_1)
| spl0_1 ),
inference(resolution,[],[f80,f6]) ).
fof(f103,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(X0,e_2,e_2) )
| spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f67,f63]) ).
fof(f105,plain,
( ~ product(e_1,e_1,e_1)
| spl0_1 ),
inference(resolution,[],[f81,f7]) ).
fof(f109,plain,
( ~ product(e_2,e_2,e_2)
| spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f92,f103]) ).
fof(f116,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f109,f44]) ).
fof(f117,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f116]) ).
fof(f126,plain,
( ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f105,f19,f30]) ).
fof(f130,plain,
( ~ spl0_7
| spl0_1 ),
inference(avatar_split_clause,[],[f102,f19,f48]) ).
fof(f131,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f48,f43]) ).
fof(f137,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f100,f30,f19]) ).
fof(f138,plain,
( ! [X0] :
( equalish(e_1,X0)
| ~ product(X0,e_2,e_2) )
| ~ spl0_1 ),
inference(resolution,[],[f20,f11]) ).
fof(f150,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f138,f6]) ).
fof(f151,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f28,f20]) ).
fof(f157,plain,
( ~ spl0_7
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f151,f27,f19,f48]) ).
fof(f158,plain,
( ~ spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f150,f19,f43]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s7,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f93]) ).
cnf(s9,plain,
( spl0_4
| ~ spl0_9 ),
inference(sat_conversion,[],[f99]) ).
cnf(s10,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s14,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f126]) ).
cnf(s18,plain,
( spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f130]) ).
cnf(s19,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f131]) ).
cnf(s21,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f137]) ).
cnf(s27,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f157]) ).
cnf(s28,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f158]) ).
cnf(s29,plain,
spl0_1,
inference(rat,[],[s7,s10,s9,s19,s14,s18]) ).
cnf(s30,plain,
~ spl0_6,
inference(rat,[],[s28,s29]) ).
cnf(s31,plain,
spl0_4,
inference(rat,[],[s21,s29]) ).
cnf(s33,plain,
spl0_7,
inference(rat,[],[s19,s30]) ).
cnf(s34,plain,
spl0_3,
inference(rat,[],[s2,s31]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s27,s29,s33,s34]) ).
fof(f159,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:33:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.17/1.50 % (2572396)Input is clausal, will run a generic CNF schedule.
% 0.17/1.50 % (2572404)lrs+10_1_sil=8000:sp=occurrence:random_seed=3553706748:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/1.50 % (2572405)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2836870924:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.17/1.50 % (2572407)dis-21_1_sil=8000:lcm=predicate:random_seed=108838698: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)
% 0.17/1.50 % (2572401)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=2782770394:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.17/1.50 % (2572402)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3333001352:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.17/1.50 % (2572403)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3793995049:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.17/1.50 % (2572405)Refutation not found, incomplete strategy
% 0.17/1.50 % (2572405)------------------------------
% 0.17/1.50 % (2572405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2572405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2572405)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2572405)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (2572405)Time elapsed: 0.001 s
% 0.17/1.50 % (2572405)Peak memory usage: 86 MB
% 0.17/1.50 % (2572406)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2937572410:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/1.50 % (2572406)First to succeed.
% 0.17/1.50 % (2572406)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2572396"
% 0.17/1.50 % (2572407)Also succeeded, but the first one will report.
% 0.17/1.50 % (2572404)Instruction limit reached!
% 0.17/1.50 % (2572404)------------------------------
% 0.17/1.50 % (2572404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2572404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2572404)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2572404)Termination reason: Instruction limit
% 0.17/1.50 % (2572404)Termination phase: Saturation
% 0.17/1.50 % (2572404)Time elapsed: 0.058 s
% 0.17/1.50 % (2572404)Peak memory usage: 88 MB
% 0.17/1.50 % (2572404)Instructions burned: 109 (million)
% 0.17/1.50 % (2572415)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=2301181703:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.17/1.50 % (2572405)------------------------------
% 0.17/1.50 % (2572405)------------------------------
% 0.17/1.50 % (2572406)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (2572406)------------------------------
% 0.17/1.50 % (2572406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2572406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2572406)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2572406)Termination reason: Refutation
% 0.17/1.50 % (2572406)Time elapsed: 0.006 s
% 0.17/1.50 % (2572406)Peak memory usage: 89 MB
% 0.17/1.50 % (2572406)Instructions burned: 5 (million)
% 0.17/1.50 % (2572406)------------------------------
% 0.17/1.50 % (2572406)------------------------------
% 0.17/1.50 % (2572396)Success in time 0.447 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------