%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP135-1.002 : 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 : 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 10:13:03 AM UTC 2026
% Result : Unsatisfiable 2.10s 0.89s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 12 unt; 5 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 128 ( 65 ~; 58 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
! [X0,X1] :
( product(X0,X1,e_2)
| ~ group_element(X1)
| product(X0,X1,e_1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f9,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f10,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f3,f8]) ).
fof(f11,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f3,f7]) ).
fof(f12,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f3,f6]) ).
fof(f16,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X2,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f10,f9]) ).
fof(f17,plain,
! [X0] :
( ~ product(e_1,X0,e_2)
| ~ group_element(X0)
| product(e_2,X0,e_1)
| ~ group_element(e_2) ),
inference(resolution,[],[f10,f5]) ).
fof(f18,plain,
! [X0] :
( ~ group_element(X0)
| ~ product(e_1,X0,e_2)
| product(e_2,X0,e_1) ),
inference(forward_subsumption_resolution,[],[f17,f2]) ).
fof(f21,plain,
! [X0] :
( ~ product(X0,e_2,e_1)
| ~ product(e_1,X0,e_2) ),
inference(factoring,[],[f16]) ).
fof(f24,definition,
( spl0_1
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f25,plain,
( product(e_1,e_1,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( ~ product(e_1,e_1,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,definition,
( spl0_2
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f29,plain,
( product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f36,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| spl0_1 ),
inference(resolution,[],[f26,f5]) ).
fof(f38,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| spl0_1 ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f39,plain,
( product(e_1,e_1,e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f38,f1]) ).
fof(f40,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f39,f24,f28]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ product(X1,e_1,X2)
| ~ product(X2,X1,X0)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f12,f9]) ).
fof(f50,definition,
( spl0_3
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f52,plain,
( product(e_1,e_2,e_1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f63,definition,
( spl0_5
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f65,plain,
( ~ product(e_1,e_2,e_2)
| spl0_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_6
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f72,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_5 ),
inference(resolution,[],[f65,f5]) ).
fof(f74,plain,
( product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f72,f2]) ).
fof(f75,plain,
( product(e_1,e_2,e_1)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f74,f1]) ).
fof(f76,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f75,f63,f50]) ).
fof(f81,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(factoring,[],[f41]) ).
fof(f82,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f81,f25]) ).
fof(f84,plain,
( ~ spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f82,f24,f67]) ).
fof(f93,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[],[f18,f1]) ).
fof(f94,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[],[f18,f2]) ).
fof(f96,plain,
( spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f93,f24,f67]) ).
fof(f117,plain,
~ product(e_1,e_2,e_2),
inference(forward_subsumption_resolution,[],[f94,f21]) ).
fof(f118,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f117,f63]) ).
fof(f125,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_3 ),
inference(resolution,[],[f52,f11]) ).
fof(f127,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f125,f29]) ).
fof(f128,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f127]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s5,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f76]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f84]) ).
cnf(s12,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f96]) ).
cnf(s17,plain,
~ spl0_5,
inference(sat_conversion,[],[f118]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f128]) ).
cnf(s20,plain,
spl0_3,
inference(rat,[],[s5,s17]) ).
cnf(s21,plain,
~ spl0_2,
inference(rat,[],[s19,s20]) ).
cnf(s22,plain,
spl0_1,
inference(rat,[],[s2,s21]) ).
cnf(s23,plain,
spl0_6,
inference(rat,[],[s12,s22]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s6,s23,s22]) ).
fof(f129,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP135-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 09:31:19 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 2.10/0.89 % (2115758)Input is clausal, will run a generic CNF schedule.
% 2.10/0.89 % (2115768)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3340054630:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.10/0.89 % (2115765)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=435504250:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.10/0.89 % (2115764)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4270679690:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.10/0.89 % (2115766)lrs+10_1_sil=8000:sp=occurrence:random_seed=412483051:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.10/0.89 % (2115769)dis-21_1_sil=8000:lcm=predicate:random_seed=2316276997: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)
% 2.10/0.89 % (2115763)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=2109908318:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.10/0.89 % (2115767)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2933166910:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.10/0.89 % (2115768)First to succeed.
% 2.10/0.89 % (2115768)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2115758"
% 2.10/0.89 % (2115769)Also succeeded, but the first one will report.
% 2.10/0.89 % (2115766)Also succeeded, but the first one will report.
% 2.10/0.89 % (2115767)Also succeeded, but the first one will report.
% 2.10/0.89 % (2115768)Refutation found. Thanks to Tanya!
% 2.10/0.89 % SZS status Unsatisfiable for theBenchmark
% 2.10/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.10/0.89 % (2115768)------------------------------
% 2.10/0.89 % (2115768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.10/0.89 % (2115768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.89 % (2115768)CaDiCaL version: 2.1.3
% 2.10/0.89 % (2115768)Termination reason: Refutation
% 2.10/0.89 % (2115768)Time elapsed: 0.003 s
% 2.10/0.89 % (2115768)Peak memory usage: 89 MB
% 2.10/0.89 % (2115768)Instructions burned: 4 (million)
% 2.10/0.89 % (2115768)------------------------------
% 2.10/0.89 % (2115768)------------------------------
% 2.10/0.89 % (2115758)Success in time 0.28 s
% 2.10/0.89 % Vampire exiting
%------------------------------------------------------------------------------