%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP135-2.002 : 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 : n018.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 3.66s 1.48s
% Output : Refutation 3.66s
% 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(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(f8,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(f9,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(f10,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(f11,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(f12,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(f14,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f6,f11]) ).
fof(f15,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f6,f10]) ).
fof(f16,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f6,f9]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X2,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f14,f12]) ).
fof(f21,plain,
! [X0] :
( ~ product(e_1,X0,e_2)
| ~ group_element(X0)
| product(e_2,X0,e_1)
| ~ group_element(e_2) ),
inference(resolution,[],[f14,f8]) ).
fof(f22,plain,
! [X0] :
( ~ group_element(X0)
| ~ product(e_1,X0,e_2)
| product(e_2,X0,e_1) ),
inference(forward_subsumption_resolution,[],[f21,f5]) ).
fof(f25,plain,
! [X0] :
( ~ product(X0,e_2,e_1)
| ~ product(e_1,X0,e_2) ),
inference(factoring,[],[f20]) ).
fof(f28,definition,
( spl0_1
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f29,plain,
( product(e_1,e_1,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( ~ product(e_1,e_1,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f32,definition,
( spl0_2
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f33,plain,
( product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f40,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| spl0_1 ),
inference(resolution,[],[f30,f8]) ).
fof(f42,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| spl0_1 ),
inference(duplicate_literal_removal,[],[f40]) ).
fof(f43,plain,
( product(e_1,e_1,e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f42,f4]) ).
fof(f44,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f43,f28,f32]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ product(X1,e_1,X2)
| ~ product(X2,X1,X0)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f16,f12]) ).
fof(f54,definition,
( spl0_3
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f56,plain,
( product(e_1,e_2,e_1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f67,definition,
( spl0_5
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f69,plain,
( ~ product(e_1,e_2,e_2)
| spl0_5 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_6
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f76,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_5 ),
inference(resolution,[],[f69,f8]) ).
fof(f78,plain,
( product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f76,f5]) ).
fof(f79,plain,
( product(e_1,e_2,e_1)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f78,f4]) ).
fof(f80,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f79,f67,f54]) ).
fof(f85,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(factoring,[],[f45]) ).
fof(f86,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f85,f29]) ).
fof(f88,plain,
( ~ spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f86,f28,f71]) ).
fof(f97,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[],[f22,f4]) ).
fof(f98,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[],[f22,f5]) ).
fof(f99,plain,
~ product(e_1,e_2,e_2),
inference(forward_subsumption_resolution,[],[f98,f25]) ).
fof(f100,plain,
( spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f97,f28,f71]) ).
fof(f103,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f99,f67]) ).
fof(f132,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_3 ),
inference(resolution,[],[f56,f15]) ).
fof(f134,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f132,f33]) ).
fof(f135,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f134]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f80]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s12,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f100]) ).
cnf(s15,plain,
~ spl0_5,
inference(sat_conversion,[],[f103]) ).
cnf(s20,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f135]) ).
cnf(s21,plain,
spl0_3,
inference(rat,[],[s5,s15]) ).
cnf(s22,plain,
~ spl0_2,
inference(rat,[],[s20,s21]) ).
cnf(s23,plain,
spl0_1,
inference(rat,[],[s2,s22]) ).
cnf(s24,plain,
spl0_6,
inference(rat,[],[s12,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s6,s24,s23]) ).
fof(f136,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n018.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 09:33:53 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 3.66/1.48 % (2074370)Input is clausal, will run a generic CNF schedule.
% 3.66/1.48 % (2074393)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=2252540777:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.66/1.48 % (2074399)dis-21_1_sil=8000:lcm=predicate:random_seed=843115334: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)
% 3.66/1.48 % (2074395)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3601294954:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.66/1.48 % (2074396)lrs+10_1_sil=8000:sp=occurrence:random_seed=3494897814:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.66/1.48 % (2074397)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2337638084:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.66/1.48 % (2074394)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2998231227:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.66/1.48 % (2074398)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=560582786:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.66/1.48 % (2074398)First to succeed.
% 3.66/1.48 % (2074398)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2074370"
% 3.66/1.48 % (2074399)Also succeeded, but the first one will report.
% 3.66/1.48 % (2074396)Also succeeded, but the first one will report.
% 3.66/1.48 % (2074397)Instruction limit reached!
% 3.66/1.48 % (2074397)------------------------------
% 3.66/1.48 % (2074397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (2074397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (2074397)CaDiCaL version: 2.1.3
% 3.66/1.48 % (2074397)Termination reason: Instruction limit
% 3.66/1.48 % (2074397)Termination phase: Saturation
% 3.66/1.48 % (2074397)Time elapsed: 0.056 s
% 3.66/1.48 % (2074397)Peak memory usage: 86 MB
% 3.66/1.48 % (2074397)Instructions burned: 116 (million)
% 3.66/1.48 % (2074407)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=3060939895:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.66/1.48 % (2074407)Also succeeded, but the first one will report.
% 3.66/1.48 % (2074398)Refutation found. Thanks to Tanya!
% 3.66/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.66/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.48 % (2074398)------------------------------
% 3.66/1.48 % (2074398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (2074398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (2074398)CaDiCaL version: 2.1.3
% 3.66/1.48 % (2074398)Termination reason: Refutation
% 3.66/1.48 % (2074398)Time elapsed: 0.005 s
% 3.66/1.48 % (2074398)Peak memory usage: 89 MB
% 3.66/1.48 % (2074398)Instructions burned: 4 (million)
% 3.66/1.48 % (2074398)------------------------------
% 3.66/1.48 % (2074398)------------------------------
% 3.66/1.48 % (2074370)Success in time 0.434 s
% 3.66/1.48 % Vampire exiting
%------------------------------------------------------------------------------