%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 10:13:01 AM UTC 2026
% Result : Unsatisfiable 0.42s 0.84s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 13 unt; 10 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 212 ( 108 ~; 94 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f5,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f7,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,X1,X0)
| ~ product(X5,X4,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_1) ).
fof(f13,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_2) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( ~ product(X2,e_1,X3)
| ~ product(X0,e_2,X1)
| ~ product(X2,e_2,X0)
| ~ product(X3,e_1,X1) ),
inference(resolution,[],[f6,f13]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_2)
| ~ product(e_1,X3,X1) ),
inference(resolution,[],[f6,f12]) ).
fof(f16,plain,
! [X0,X1] :
( ~ product(X0,e_1,X0)
| ~ product(X1,e_2,X0)
| ~ product(X0,e_2,X1) ),
inference(factoring,[],[f14]) ).
fof(f20,plain,
! [X0,X1] :
( ~ product(e_2,X0,e_2)
| ~ product(e_2,X1,e_1)
| ~ product(e_1,X1,e_2) ),
inference(factoring,[],[f15]) ).
fof(f22,definition,
( spl0_1
<=> ! [X1] :
( ~ product(e_2,X1,e_1)
| ~ product(e_1,X1,e_2) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f23,plain,
( ! [X1] :
( ~ product(e_2,X1,e_1)
| ~ product(e_1,X1,e_2) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,definition,
( spl0_2
<=> ! [X0] : ~ product(e_2,X0,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f26,plain,
( ! [X0] : ~ product(e_2,X0,e_2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f20,f25,f22]) ).
fof(f31,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2) ),
inference(resolution,[],[f8,f4]) ).
fof(f32,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,X0,e_1)
| product(X0,X0,e_2) ),
inference(factoring,[],[f8]) ).
fof(f33,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2) ),
inference(resolution,[],[f5,f8]) ).
fof(f34,plain,
( ! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f33,f26]) ).
fof(f35,plain,
( product(e_2,e_1,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f34,f4]) ).
fof(f36,plain,
( product(e_2,e_2,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f34,f5]) ).
fof(f41,plain,
( ! [X0] :
( equalish(e_1,X0)
| ~ product(e_2,X0,e_1) )
| ~ spl0_2 ),
inference(resolution,[],[f35,f10]) ).
fof(f49,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[],[f32,f5]) ).
fof(f51,definition,
( spl0_3
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f53,plain,
( product(e_1,e_1,e_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl0_4
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f57,plain,
( product(e_1,e_1,e_1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f62,plain,
( ! [X0] :
( equalish(e_1,X0)
| ~ product(X0,e_1,e_2) )
| ~ spl0_3 ),
inference(resolution,[],[f53,f11]) ).
fof(f65,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f41,f6]) ).
fof(f66,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f65,f36]) ).
fof(f67,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f66]) ).
fof(f69,definition,
( spl0_5
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f71,plain,
( product(e_2,e_2,e_2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f73,definition,
( spl0_6
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f76,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f49,f73,f69]) ).
fof(f79,plain,
( ! [X0] :
( equalish(e_2,X0)
| ~ product(X0,e_2,e_2) )
| ~ spl0_5 ),
inference(resolution,[],[f71,f11]) ).
fof(f83,definition,
( spl0_7
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f84,plain,
( product(e_1,e_2,e_1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f88,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[],[f31,f4]) ).
fof(f89,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[],[f31,f5]) ).
fof(f91,definition,
( spl0_8
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f93,plain,
( product(e_1,e_2,e_2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f89,f83,f91]) ).
fof(f97,plain,
( ! [X0] :
( equalish(e_2,X0)
| ~ product(e_1,X0,e_1) )
| ~ spl0_7 ),
inference(resolution,[],[f84,f10]) ).
fof(f101,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[],[f33,f4]) ).
fof(f104,definition,
( spl0_9
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f108,definition,
( spl0_10
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f110,plain,
( product(e_2,e_1,e_1)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f101,f108,f104]) ).
fof(f113,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_7 ),
inference(resolution,[],[f97,f7]) ).
fof(f124,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_3 ),
inference(resolution,[],[f62,f6]) ).
fof(f127,plain,
( ~ spl0_9
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f124,f51,f104]) ).
fof(f129,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_1
| ~ spl0_10 ),
inference(resolution,[],[f110,f23]) ).
fof(f142,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f113,f83,f55]) ).
fof(f143,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f88,f55,f51]) ).
fof(f144,plain,
( ~ spl0_3
| ~ spl0_1
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f129,f108,f22,f51]) ).
fof(f148,plain,
( ! [X0] :
( ~ product(e_1,e_2,X0)
| ~ product(X0,e_2,e_1) )
| ~ spl0_4 ),
inference(resolution,[],[f57,f16]) ).
fof(f156,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_4
| ~ spl0_8 ),
inference(resolution,[],[f93,f148]) ).
fof(f163,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_5 ),
inference(resolution,[],[f79,f7]) ).
fof(f164,plain,
( $false
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f163,f93]) ).
fof(f165,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f164]) ).
fof(f166,plain,
( ~ spl0_6
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f156,f91,f55,f73]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f67]) ).
cnf(s5,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s7,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f94]) ).
cnf(s9,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f111]) ).
cnf(s11,plain,
( ~ spl0_3
| ~ spl0_9 ),
inference(sat_conversion,[],[f127]) ).
cnf(s14,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f142]) ).
cnf(s15,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f143]) ).
cnf(s16,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10 ),
inference(sat_conversion,[],[f144]) ).
cnf(s18,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f165]) ).
cnf(s19,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f166]) ).
cnf(s21,plain,
spl0_1,
inference(rat,[],[s1,s4]) ).
cnf(s22,plain,
~ spl0_4,
inference(rat,[],[s5,s19,s18,s7,s14]) ).
cnf(s23,plain,
spl0_3,
inference(rat,[],[s15,s22]) ).
cnf(s24,plain,
~ spl0_10,
inference(rat,[],[s16,s21,s23]) ).
cnf(s25,plain,
~ spl0_9,
inference(rat,[],[s11,s23]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s9,s24,s25]) ).
fof(f168,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 09:30:19 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.34 Running first-order theorem proving
% 0.07/0.34 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
% 0.42/0.84 % (2113616)Input is clausal, will run a generic CNF schedule.
% 0.42/0.84 % (2113625)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=608630286:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.42/0.84 % (2113622)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=202730024:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.42/0.84 % (2113621)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=2364962739:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.42/0.84 % (2113626)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2692020253:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.42/0.84 % (2113623)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=969865031:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.42/0.84 % (2113627)dis-21_1_sil=8000:lcm=predicate:random_seed=448453523: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)
% 0.42/0.84 % (2113624)lrs+10_1_sil=8000:sp=occurrence:random_seed=2945579849:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.42/0.84 % (2113625)Refutation not found, incomplete strategy
% 0.42/0.84 % (2113625)------------------------------
% 0.42/0.84 % (2113625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.84 % (2113625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.84 % (2113625)CaDiCaL version: 2.1.3
% 0.42/0.84 % (2113625)Termination reason: Refutation not found, incomplete strategy
% 0.42/0.84 % (2113625)Time elapsed: 0.0000 s
% 0.42/0.84 % (2113625)Peak memory usage: 86 MB
% 0.42/0.84 % (2113626)First to succeed.
% 0.42/0.84 % (2113626)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2113616"
% 0.42/0.84 % (2113627)Also succeeded, but the first one will report.
% 0.42/0.84 % (2113624)Instruction limit reached!
% 0.42/0.84 % (2113624)------------------------------
% 0.42/0.84 % (2113624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.84 % (2113624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.84 % (2113624)CaDiCaL version: 2.1.3
% 0.42/0.84 % (2113624)Termination reason: Instruction limit
% 0.42/0.84 % (2113624)Termination phase: Saturation
% 0.42/0.84 % (2113624)Time elapsed: 0.032 s
% 0.42/0.84 % (2113624)Peak memory usage: 88 MB
% 0.42/0.84 % (2113624)Instructions burned: 109 (million)
% 0.42/0.84 % (2113625)------------------------------
% 0.42/0.84 % (2113625)------------------------------
% 0.42/0.84 % (2113626)Refutation found. Thanks to Tanya!
% 0.42/0.84 % SZS status Unsatisfiable for theBenchmark
% 0.42/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/0.93 % (2113626)------------------------------
% 2.31/0.93 % (2113626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.93 % (2113626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.93 % (2113626)CaDiCaL version: 2.1.3
% 2.31/0.93 % (2113626)Termination reason: Refutation
% 2.31/0.93 % (2113626)Time elapsed: 0.003 s
% 2.31/0.93 % (2113626)Peak memory usage: 89 MB
% 2.31/0.93 % (2113626)Instructions burned: 5 (million)
% 2.31/0.93 % (2113626)------------------------------
% 2.31/0.93 % (2113626)------------------------------
% 2.31/0.93 % (2113616)Success in time 0.298 s
% 2.31/0.93 % Vampire exiting
%------------------------------------------------------------------------------