%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 10:13:00 AM UTC 2026
% Result : Unsatisfiable 3.37s 1.37s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 11 unt; 5 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 175 ( 72 ~; 98 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( product(X0,e_3,X1)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
fof(f3,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X0,X1,X2)
| ~ product(X3,X1,X0)
| ~ product(X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f8,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f14,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f17,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(f18,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f19,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f8,f17]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X1,X2,e_2)
| ~ product(X1,X0,X2) ),
inference(resolution,[],[f19,f18]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,e_2)
| ~ product(e_1,X0,X1)
| ~ product(e_2,X1,X2) ),
inference(resolution,[],[f19,f3]) ).
fof(f56,plain,
! [X0] :
( ~ product(e_1,X0,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(factoring,[],[f37]) ).
fof(f58,definition,
( spl0_1
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f60,plain,
( ~ product(e_1,e_1,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl0_2
<=> ! [X0] : ~ product(e_1,X0,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f63,plain,
( ! [X0] : ~ product(e_1,X0,e_1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f56,f62,f58]) ).
fof(f74,plain,
( ! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(e_2,X0,e_1) )
| spl0_1 ),
inference(resolution,[],[f60,f18]) ).
fof(f87,plain,
( ~ product(e_2,e_3,e_1)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| spl0_1 ),
inference(resolution,[],[f74,f14]) ).
fof(f88,plain,
( ~ product(e_2,e_1,e_1)
| spl0_1 ),
inference(factoring,[],[f74]) ).
fof(f89,plain,
( ~ product(e_2,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f87,f5]) ).
fof(f90,plain,
( ~ product(e_2,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f89,f6]) ).
fof(f92,definition,
( spl0_3
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f96,definition,
( spl0_4
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f97,plain,
( ~ product(e_2,e_1,e_1)
| spl0_4 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f100,definition,
( spl0_5
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f102,plain,
( ~ product(e_2,e_3,e_1)
| spl0_5 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_3
| spl0_4
| ~ spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f90,f58,f100,f96,f92]) ).
fof(f111,plain,
( ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f88,f58,f96]) ).
fof(f121,plain,
( ! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(X0,e_1,e_2) )
| spl0_4 ),
inference(resolution,[],[f97,f3]) ).
fof(f122,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| ~ group_element(e_2)
| spl0_5 ),
inference(resolution,[],[f102,f2]) ).
fof(f126,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| ~ group_element(e_2)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f122,f5]) ).
fof(f127,plain,
( product(e_2,e_2,e_1)
| ~ group_element(e_2)
| spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f126,f97]) ).
fof(f128,plain,
( product(e_2,e_2,e_1)
| spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f127,f6]) ).
fof(f212,plain,
( ~ product(e_2,e_1,e_2)
| spl0_4 ),
inference(factoring,[],[f121]) ).
fof(f213,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f212,f96,f92]) ).
fof(f238,plain,
! [X0] :
( ~ product(e_1,X0,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(factoring,[],[f39]) ).
fof(f240,plain,
( ! [X0] : ~ product(e_1,X0,e_2)
| spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f238,f128]) ).
fof(f246,plain,
( ~ group_element(e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| spl0_4
| spl0_5 ),
inference(resolution,[],[f240,f2]) ).
fof(f247,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f246,f6]) ).
fof(f248,plain,
( product(e_1,e_1,e_2)
| ~ group_element(e_1)
| spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f247,f240]) ).
fof(f249,plain,
( ~ group_element(e_1)
| spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f248,f240]) ).
fof(f250,plain,
( $false
| spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f249,f5]) ).
fof(f251,plain,
( spl0_4
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f297,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| ~ group_element(e_1)
| ~ spl0_2 ),
inference(resolution,[],[f63,f2]) ).
fof(f298,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f297]) ).
fof(f299,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f298,f5]) ).
fof(f300,plain,
( product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f299,f63]) ).
fof(f301,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f300,f63]) ).
fof(f302,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f301]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
( spl0_1
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f103]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f111]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f213]) ).
cnf(s7,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f251]) ).
cnf(s12,plain,
~ spl0_2,
inference(sat_conversion,[],[f302]) ).
cnf(s13,plain,
~ spl0_1,
inference(rat,[],[s1,s12]) ).
cnf(s14,plain,
~ spl0_4,
inference(rat,[],[s3,s13]) ).
cnf(s15,plain,
spl0_5,
inference(rat,[],[s7,s14]) ).
cnf(s16,plain,
~ spl0_3,
inference(rat,[],[s5,s14]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s2,s13,s14,s15,s16]) ).
fof(f303,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n006.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:28:56 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.37/1.37 % (2730206)Input is clausal, will run a generic CNF schedule.
% 3.37/1.37 % (2730212)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3972834059:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.37/1.37 % (2730211)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=475739176:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.37/1.37 % (2730217)dis-21_1_sil=8000:lcm=predicate:random_seed=248634063: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)
% 3.37/1.37 % (2730213)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2335873948:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.37/1.37 % (2730214)lrs+10_1_sil=8000:sp=occurrence:random_seed=4051827185:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.37/1.37 % (2730215)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1673199348:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.37/1.37 % (2730216)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3664295579:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.37/1.37 % (2730214)Refutation not found, incomplete strategy
% 3.37/1.37 % (2730214)------------------------------
% 3.37/1.37 % (2730214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.37 % (2730214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.37 % (2730214)CaDiCaL version: 2.1.3
% 3.37/1.37 % (2730214)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.37 % (2730214)Time elapsed: 0.001 s
% 3.37/1.37 % (2730214)Peak memory usage: 87 MB
% 3.37/1.37 % (2730216)First to succeed.
% 3.37/1.37 % (2730216)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2730206"
% 3.37/1.37 % (2730217)Also succeeded, but the first one will report.
% 3.37/1.37 % (2730215)Instruction limit reached!
% 3.37/1.37 % (2730215)------------------------------
% 3.37/1.37 % (2730215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.37 % (2730215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.37 % (2730215)CaDiCaL version: 2.1.3
% 3.37/1.37 % (2730215)Termination reason: Instruction limit
% 3.37/1.37 % (2730215)Termination phase: Saturation
% 3.37/1.37 % (2730215)Time elapsed: 0.061 s
% 3.37/1.37 % (2730215)Peak memory usage: 88 MB
% 3.37/1.37 % (2730215)Instructions burned: 114 (million)
% 3.37/1.37 % (2730225)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=3999124632:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.37/1.37 % (2730225)Also succeeded, but the first one will report.
% 3.37/1.37 % (2730214)------------------------------
% 3.37/1.37 % (2730214)------------------------------
% 3.37/1.37 % (2730216)Refutation found. Thanks to Tanya!
% 3.37/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.37/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.37 % (2730216)------------------------------
% 3.37/1.37 % (2730216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.37 % (2730216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.37 % (2730216)CaDiCaL version: 2.1.3
% 3.37/1.37 % (2730216)Termination reason: Refutation
% 3.37/1.37 % (2730216)Time elapsed: 0.009 s
% 3.37/1.37 % (2730216)Peak memory usage: 89 MB
% 3.37/1.37 % (2730216)Instructions burned: 10 (million)
% 3.37/1.37 % (2730216)------------------------------
% 3.37/1.37 % (2730216)------------------------------
% 3.37/1.37 % (2730206)Success in time 0.406 s
% 3.37/1.37 % Vampire exiting
%------------------------------------------------------------------------------