%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP132-1.002 : 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 : n019.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 0.38s 0.89s
% Output : Refutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 13 unt; 7 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 226 ( 108 ~; 111 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 44 !; 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(f4,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f5,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f9,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X0,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_1) ).
fof(f10,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_2) ).
fof(f11,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_1,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_2)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f3,f10]) ).
fof(f12,plain,
! [X2,X3,X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(X2,e_1,X3)
| ~ product(X2,e_2,X0)
| ~ product(e_1,X3,X1) ),
inference(resolution,[],[f3,f9]) ).
fof(f13,plain,
! [X0] :
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) ),
inference(factoring,[],[f11]) ).
fof(f16,definition,
( spl0_1
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f17,plain,
( product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( ~ product(e_1,e_2,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f24,definition,
( spl0_3
<=> ! [X0] :
( ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f25,plain,
( ! [X0] :
( ~ product(X0,e_2,e_1)
| ~ product(e_1,X0,e_2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f27,definition,
( spl0_4
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f28,plain,
( product(e_1,e_1,e_1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f29,plain,
( ~ product(e_1,e_1,e_1)
| spl0_4 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f30,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f13,f27,f24]) ).
fof(f41,definition,
( spl0_6
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f42,plain,
( product(e_2,e_2,e_2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f46,definition,
( spl0_7
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f47,plain,
( product(e_2,e_2,e_1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f54,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2) ),
inference(resolution,[],[f5,f1]) ).
fof(f55,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,X0,e_1)
| product(X0,X0,e_2) ),
inference(factoring,[],[f5]) ).
fof(f56,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2) ),
inference(resolution,[],[f2,f5]) ).
fof(f57,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[],[f55,f1]) ).
fof(f60,plain,
( product(e_1,e_1,e_2)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f57,f29]) ).
fof(f64,plain,
( ! [X0,X1] :
( ~ product(e_1,X1,e_2)
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_1,X1) )
| ~ spl0_6 ),
inference(resolution,[],[f42,f12]) ).
fof(f69,plain,
( ! [X0] :
( ~ product(X0,e_1,e_2)
| equalish(e_1,X0) )
| spl0_4 ),
inference(resolution,[],[f60,f8]) ).
fof(f74,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[],[f54,f2]) ).
fof(f75,plain,
( product(e_1,e_2,e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f74,f18]) ).
fof(f76,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[],[f56,f1]) ).
fof(f77,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[],[f56,f2]) ).
fof(f79,definition,
( spl0_9
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f81,plain,
( product(e_2,e_1,e_2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl0_10
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f85,plain,
( product(e_2,e_1,e_1)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f76,f83,f79]) ).
fof(f87,plain,
( ! [X0] :
( ~ product(X0,e_2,e_1)
| equalish(e_1,X0) )
| spl0_1 ),
inference(resolution,[],[f75,f8]) ).
fof(f88,plain,
( ! [X0] :
( ~ product(e_1,X0,e_1)
| equalish(e_2,X0) )
| spl0_1 ),
inference(resolution,[],[f75,f7]) ).
fof(f95,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(X0,e_2,e_2) )
| spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f64,f60]) ).
fof(f102,plain,
( equalish(e_1,e_2)
| spl0_4
| ~ spl0_9 ),
inference(resolution,[],[f81,f69]) ).
fof(f107,plain,
( $false
| spl0_4
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f102,f3]) ).
fof(f108,plain,
( spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f107]) ).
fof(f114,plain,
( ~ product(e_2,e_2,e_2)
| spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f85,f95]) ).
fof(f120,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f114,f42]) ).
fof(f121,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f131,plain,
( equalish(e_2,e_1)
| spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f28,f88]) ).
fof(f136,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f131,f4]) ).
fof(f137,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f136]) ).
fof(f140,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f77,f46,f41]) ).
fof(f142,plain,
( equalish(e_1,e_2)
| spl0_1
| ~ spl0_7 ),
inference(resolution,[],[f47,f87]) ).
fof(f144,plain,
( ! [X0] :
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1) )
| ~ spl0_7 ),
inference(resolution,[],[f47,f7]) ).
fof(f146,plain,
( $false
| spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f142,f3]) ).
fof(f147,plain,
( spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f153,plain,
( ! [X0] :
( equalish(e_1,X0)
| ~ product(X0,e_2,e_2) )
| ~ spl0_1 ),
inference(resolution,[],[f17,f8]) ).
fof(f157,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_7 ),
inference(resolution,[],[f144,f4]) ).
fof(f168,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f153,f3]) ).
fof(f171,plain,
( ~ spl0_10
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f157,f46,f83]) ).
fof(f174,plain,
( ~ spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f168,f16,f41]) ).
fof(f176,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_3
| ~ spl0_7 ),
inference(resolution,[],[f47,f25]) ).
fof(f180,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f176,f17]) ).
fof(f181,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f180]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f30]) ).
cnf(s7,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f86]) ).
cnf(s8,plain,
( spl0_4
| ~ spl0_9 ),
inference(sat_conversion,[],[f108]) ).
cnf(s10,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_10 ),
inference(sat_conversion,[],[f121]) ).
cnf(s15,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f137]) ).
cnf(s18,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f140]) ).
cnf(s19,plain,
( spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( ~ spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f171]) ).
cnf(s27,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f174]) ).
cnf(s28,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f181]) ).
cnf(s29,plain,
spl0_1,
inference(rat,[],[s7,s10,s8,s18,s15,s19]) ).
cnf(s30,plain,
~ spl0_6,
inference(rat,[],[s27,s29]) ).
cnf(s32,plain,
spl0_7,
inference(rat,[],[s18,s30]) ).
cnf(s33,plain,
~ spl0_10,
inference(rat,[],[s25,s32]) ).
cnf(s35,plain,
~ spl0_3,
inference(rat,[],[s28,s29,s32]) ).
cnf(s36,plain,
spl0_9,
inference(rat,[],[s7,s33]) ).
cnf(s37,plain,
~ spl0_4,
inference(rat,[],[s2,s35]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s8,s36,s37]) ).
fof(f182,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP132-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:31:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.38/0.89 % (2831717)Input is clausal, will run a generic CNF schedule.
% 0.38/0.89 % (2831727)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=893867390:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.38/0.89 % (2831727)First to succeed.
% 0.38/0.89 % (2831727)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2831717"
% 0.38/0.89 % (2831725)lrs+10_1_sil=8000:sp=occurrence:random_seed=1167206443:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.38/0.89 % (2831724)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4110252646:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.38/0.89 % (2831728)dis-21_1_sil=8000:lcm=predicate:random_seed=2767705911: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)
% 0.38/0.89 % (2831723)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2688079306:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.38/0.89 % (2831726)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2199269561:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.38/0.89 % (2831722)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=3153413883:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.38/0.89 % (2831726)Refutation not found, incomplete strategy
% 0.38/0.89 % (2831726)------------------------------
% 0.38/0.89 % (2831726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.38/0.89 % (2831726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.89 % (2831726)CaDiCaL version: 2.1.3
% 0.38/0.89 % (2831726)Termination reason: Refutation not found, incomplete strategy
% 0.38/0.89 % (2831726)Time elapsed: 0.001 s
% 0.38/0.89 % (2831726)Peak memory usage: 86 MB
% 0.38/0.89 % (2831728)Also succeeded, but the first one will report.
% 0.38/0.89 % (2831725)Instruction limit reached!
% 0.38/0.89 % (2831725)------------------------------
% 0.38/0.89 % (2831725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.38/0.89 % (2831725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.89 % (2831725)CaDiCaL version: 2.1.3
% 0.38/0.89 % (2831725)Termination reason: Instruction limit
% 0.38/0.89 % (2831725)Termination phase: Saturation
% 0.38/0.89 % (2831725)Time elapsed: 0.059 s
% 0.38/0.89 % (2831725)Peak memory usage: 88 MB
% 0.38/0.89 % (2831725)Instructions burned: 107 (million)
% 0.38/0.89 % (2831727)Refutation found. Thanks to Tanya!
% 0.38/0.89 % SZS status Unsatisfiable for theBenchmark
% 0.38/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.29/0.99 % (2831727)------------------------------
% 2.29/0.99 % (2831727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/0.99 % (2831727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/0.99 % (2831727)CaDiCaL version: 2.1.3
% 2.29/0.99 % (2831727)Termination reason: Refutation
% 2.29/0.99 % (2831727)Time elapsed: 0.003 s
% 2.29/0.99 % (2831727)Peak memory usage: 89 MB
% 2.29/0.99 % (2831727)Instructions burned: 5 (million)
% 2.29/0.99 % (2831727)------------------------------
% 2.29/0.99 % (2831727)------------------------------
% 2.29/0.99 % (2831717)Success in time 0.288 s
% 2.29/0.99 % Vampire exiting
%------------------------------------------------------------------------------