%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-7.003 : 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 : n011.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 3.57s 1.48s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 55 ( 19 unt; 3 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 126 ( 59 ~; 64 |; 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 : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f12,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f15,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f16,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/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f20,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f25,axiom,
! [X0] : product2(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f26,negated_conjecture,
! [X2,X3,X0,X1] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
fof(f29,plain,
! [X0,X1] :
( ~ product1(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f18,f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ product1(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f19,f20]) ).
fof(f34,plain,
! [X2,X3,X0,X1,X4] :
( ~ product2(X0,X1,X2)
| equalish(X2,X3)
| ~ product1(X4,X3,X0)
| ~ product1(X1,X3,X4) ),
inference(resolution,[],[f22,f26]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ product1(X2,X1,X0)
| equalish(X0,X1)
| ~ product1(X0,X1,X2) ),
inference(resolution,[],[f34,f25]) ).
fof(f39,plain,
! [X2,X3,X0,X1,X4] :
( ~ product2(X0,X1,X2)
| equalish(X1,X3)
| ~ product1(X4,X2,X0)
| ~ product1(X3,X2,X4) ),
inference(resolution,[],[f23,f26]) ).
fof(f43,plain,
! [X0,X1] :
( ~ product1(X0,X1,X0)
| equalish(X0,X1) ),
inference(factoring,[],[f38]) ).
fof(f52,plain,
! [X0] :
( ~ group_element(X0)
| product1(e_3,X0,e_1)
| product1(e_3,X0,e_2)
| ~ group_element(e_3)
| equalish(e_3,X0) ),
inference(resolution,[],[f16,f43]) ).
fof(f55,plain,
! [X0] :
( product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(e_3,X0) ),
inference(forward_subsumption_resolution,[],[f52,f9]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ product1(X2,X0,X0)
| equalish(X0,X1)
| ~ product1(X1,X0,X2) ),
inference(resolution,[],[f39,f25]) ).
fof(f71,plain,
! [X0,X1] :
( ~ product1(X1,X0,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f67,f20]) ).
fof(f79,definition,
( spl0_1
<=> product1(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f80,plain,
( product1(e_3,e_2,e_1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f87,plain,
( equalish(e_2,e_3)
| product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_3,e_2) ),
inference(resolution,[],[f71,f55]) ).
fof(f88,plain,
( product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f87,f13]) ).
fof(f90,plain,
( product1(e_3,e_2,e_1)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f88,f8]) ).
fof(f91,plain,
product1(e_3,e_2,e_1),
inference(forward_subsumption_resolution,[],[f90,f15]) ).
fof(f92,plain,
spl0_1,
inference(avatar_split_clause,[],[f91,f79]) ).
fof(f96,plain,
( equalish(e_1,e_2)
| ~ product1(e_1,e_2,e_3)
| ~ spl0_1 ),
inference(resolution,[],[f80,f38]) ).
fof(f100,plain,
( ~ product1(e_1,e_2,e_3)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f96,f10]) ).
fof(f101,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,[],[f100,f16]) ).
fof(f102,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,[],[f101,f8]) ).
fof(f103,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f102,f7]) ).
fof(f105,definition,
( spl0_3
<=> product1(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f106,plain,
( product1(e_1,e_2,e_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,definition,
( spl0_4
<=> product1(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f109,plain,
( product1(e_1,e_2,e_1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( spl0_3
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f103,f79,f108,f105]) ).
fof(f120,plain,
( equalish(e_1,e_2)
| ~ spl0_3 ),
inference(resolution,[],[f106,f32]) ).
fof(f125,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f120,f10]) ).
fof(f126,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f131,plain,
( equalish(e_2,e_1)
| ~ spl0_4 ),
inference(resolution,[],[f109,f29]) ).
fof(f135,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f131,f12]) ).
fof(f136,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f135]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f92]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f126]) ).
cnf(s7,plain,
~ spl0_4,
inference(sat_conversion,[],[f136]) ).
cnf(s8,plain,
~ spl0_1,
inference(rat,[],[s3,s7,s5]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s8]) ).
fof(f137,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n011.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 09:20:30 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.57/1.48 % (2141088)Input is clausal, will run a generic CNF schedule.
% 3.57/1.48 % (2141095)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3487090676:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.57/1.48 % (2141094)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3988823528:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.57/1.48 % (2141096)lrs+10_1_sil=8000:sp=occurrence:random_seed=659317246:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.57/1.48 % (2141097)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2142649030:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.57/1.48 % (2141093)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=774516028:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.57/1.48 % (2141099)dis-21_1_sil=8000:lcm=predicate:random_seed=550018986: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)
% 3.57/1.48 % (2141097)First to succeed.
% 3.57/1.48 % (2141097)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2141088"
% 3.57/1.48 % (2141099)Also succeeded, but the first one will report.
% 3.57/1.48 % (2141096)Also succeeded, but the first one will report.
% 3.57/1.48 % (2141098)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2788308136:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.57/1.48 % (2141098)Also succeeded, but the first one will report.
% 3.57/1.48 % (2141097)Refutation found. Thanks to Tanya!
% 3.57/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.57/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.48 % (2141097)------------------------------
% 3.57/1.48 % (2141097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.48 % (2141097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.48 % (2141097)CaDiCaL version: 2.1.3
% 3.57/1.48 % (2141097)Termination reason: Refutation
% 3.57/1.48 % (2141097)Time elapsed: 0.004 s
% 3.57/1.48 % (2141097)Peak memory usage: 89 MB
% 3.57/1.48 % (2141097)Instructions burned: 4 (million)
% 3.57/1.48 % (2141097)------------------------------
% 3.57/1.48 % (2141097)------------------------------
% 3.57/1.48 % (2141088)Success in time 0.431 s
% 3.57/1.48 % Vampire exiting
%------------------------------------------------------------------------------