%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-8.003 : 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 : 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 10:12:40 AM UTC 2026
% Result : Unsatisfiable 3.51s 1.39s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 51 ( 19 unt; 3 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 53 ~; 58 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f22,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f23,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f25,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f26,axiom,
! [X0,X1] :
( product1(X0,X1,e_3)
| ~ group_element(X1)
| product1(X0,X1,e_1)
| product1(X0,X1,e_2)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f30,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f32,axiom,
! [X2,X3,X0,X1] :
( ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f33,axiom,
! [X2,X3,X0,X1] :
( ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f35,axiom,
! [X0] : product2(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f36,negated_conjecture,
! [X2,X3,X0,X1] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
fof(f50,plain,
! [X2,X3,X0,X1,X4] :
( ~ product2(X0,X1,X2)
| equalish(X2,X3)
| ~ product1(X4,X3,X0)
| ~ product1(X1,X3,X4) ),
inference(resolution,[],[f32,f36]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ product1(X2,X1,X0)
| equalish(X0,X1)
| ~ product1(X0,X1,X2) ),
inference(resolution,[],[f50,f35]) ).
fof(f55,plain,
! [X2,X3,X0,X1,X4] :
( ~ product2(X0,X1,X2)
| equalish(X1,X3)
| ~ product1(X4,X2,X0)
| ~ product1(X3,X2,X4) ),
inference(resolution,[],[f33,f36]) ).
fof(f59,plain,
! [X0,X1] :
( ~ product1(X0,X1,X0)
| equalish(X0,X1) ),
inference(factoring,[],[f54]) ).
fof(f69,plain,
! [X0] :
( equalish(e_3,X0)
| ~ group_element(X0)
| product1(e_3,X0,e_1)
| product1(e_3,X0,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f59,f26]) ).
fof(f70,plain,
! [X0] :
( product1(e_3,X0,e_2)
| ~ group_element(X0)
| product1(e_3,X0,e_1)
| equalish(e_3,X0) ),
inference(forward_subsumption_resolution,[],[f69,f19]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ product1(X2,X0,X0)
| equalish(X0,X1)
| ~ product1(X1,X0,X2) ),
inference(resolution,[],[f55,f35]) ).
fof(f98,plain,
! [X0,X1] :
( ~ product1(X1,X0,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f93,f30]) ).
fof(f106,definition,
( spl0_1
<=> product1(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f107,plain,
( product1(e_3,e_2,e_1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f117,plain,
( equalish(e_2,e_3)
| ~ group_element(e_2)
| product1(e_3,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[],[f98,f70]) ).
fof(f118,plain,
( ~ group_element(e_2)
| product1(e_3,e_2,e_1)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f117,f23]) ).
fof(f120,plain,
( product1(e_3,e_2,e_1)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f118,f18]) ).
fof(f121,plain,
product1(e_3,e_2,e_1),
inference(forward_subsumption_resolution,[],[f120,f25]) ).
fof(f122,plain,
spl0_1,
inference(avatar_split_clause,[],[f121,f106]) ).
fof(f123,plain,
( equalish(e_1,e_2)
| ~ product1(e_1,e_2,e_3)
| ~ spl0_1 ),
inference(resolution,[],[f107,f54]) ).
fof(f127,plain,
( ~ product1(e_1,e_2,e_3)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f123,f20]) ).
fof(f128,plain,
( ~ group_element(e_2)
| product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_1 ),
inference(resolution,[],[f127,f26]) ).
fof(f129,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f128,f18]) ).
fof(f130,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f129,f17]) ).
fof(f132,definition,
( spl0_3
<=> product1(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f133,plain,
( product1(e_1,e_2,e_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,definition,
( spl0_4
<=> product1(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f136,plain,
( product1(e_1,e_2,e_1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f137,plain,
( spl0_3
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f130,f106,f135,f132]) ).
fof(f146,plain,
( equalish(e_2,e_1)
| ~ spl0_3 ),
inference(resolution,[],[f133,f98]) ).
fof(f148,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f146,f22]) ).
fof(f149,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f148]) ).
fof(f154,plain,
( equalish(e_1,e_2)
| ~ spl0_4 ),
inference(resolution,[],[f136,f59]) ).
fof(f155,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f154,f20]) ).
fof(f156,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f155]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f122]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f137]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f149]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f156]) ).
cnf(s6,plain,
~ spl0_1,
inference(rat,[],[s3,s5,s4]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6]) ).
fof(f157,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:20:08 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.51/1.39 % (3248362)Input is clausal, will run a generic CNF schedule.
% 3.51/1.39 % (3248367)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=1377267870:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.51/1.39 % (3248370)lrs+10_1_sil=8000:sp=occurrence:random_seed=1129235884:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.51/1.39 % (3248369)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2311955935:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.51/1.39 % (3248368)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1420903975:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.51/1.39 % (3248371)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1046499617:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.51/1.39 % (3248371)First to succeed.
% 3.51/1.39 % (3248371)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3248362"
% 3.51/1.39 % (3248370)Also succeeded, but the first one will report.
% 3.51/1.39 % (3248373)dis-21_1_sil=8000:lcm=predicate:random_seed=253400547: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)
% 3.51/1.39 % (3248372)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2587134165:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.51/1.39 % (3248372)Also succeeded, but the first one will report.
% 3.51/1.39 % (3248373)Also succeeded, but the first one will report.
% 3.51/1.39 % (3248371)Refutation found. Thanks to Tanya!
% 3.51/1.39 % SZS status Unsatisfiable for theBenchmark
% 3.51/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.39 % (3248371)------------------------------
% 3.51/1.39 % (3248371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (3248371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (3248371)CaDiCaL version: 2.1.3
% 3.51/1.39 % (3248371)Termination reason: Refutation
% 3.51/1.39 % (3248371)Time elapsed: 0.005 s
% 3.51/1.39 % (3248371)Peak memory usage: 88 MB
% 3.51/1.39 % (3248371)Instructions burned: 5 (million)
% 3.51/1.39 % (3248371)------------------------------
% 3.51/1.39 % (3248371)------------------------------
% 3.51/1.39 % (3248362)Success in time 0.428 s
% 3.51/1.39 % Vampire exiting
%------------------------------------------------------------------------------