%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 10:16:44 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.47s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 54 ( 21 unt; 4 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 49 ~; 61 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 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(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f8,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f11,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f12,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(f14,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(f15,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(f16,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f18,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(f21,axiom,
! [X0] : product2(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f22,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2)
| product2(X3,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
fof(f27,plain,
! [X0,X1] :
( ~ product1(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f14,f16]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product1(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f15,f16]) ).
fof(f30,plain,
! [X0,X1] :
( ~ product2(X0,X0,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f18,f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ product1(X2,X0,X1)
| product1(X1,X0,e_1)
| product1(X1,X0,e_2)
| ~ group_element(X1)
| ~ group_element(X0)
| product2(e_3,X2,X0) ),
inference(resolution,[],[f12,f22]) ).
fof(f42,plain,
! [X0] :
( ~ group_element(X0)
| product1(e_3,X0,e_1)
| product1(e_3,X0,e_2)
| ~ group_element(e_3)
| equalish(X0,e_3) ),
inference(resolution,[],[f12,f27]) ).
fof(f45,plain,
! [X0] :
( product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3) ),
inference(forward_subsumption_resolution,[],[f42,f5]) ).
fof(f284,plain,
( product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[],[f45,f28]) ).
fof(f297,plain,
( product1(e_3,e_2,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f284,f4]) ).
fof(f300,plain,
( product1(e_3,e_2,e_1)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f297,f9]) ).
fof(f306,definition,
( spl0_16
<=> product1(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f308,plain,
( product1(e_3,e_2,e_1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f310,plain,
product1(e_3,e_2,e_1),
inference(forward_subsumption_resolution,[],[f300,f11]) ).
fof(f311,plain,
spl0_16,
inference(avatar_split_clause,[],[f310,f306]) ).
fof(f316,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ group_element(e_2)
| product2(e_3,e_3,e_2)
| ~ spl0_16 ),
inference(resolution,[],[f308,f39]) ).
fof(f321,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| ~ group_element(e_2)
| product2(e_3,e_3,e_2)
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f316,f3]) ).
fof(f322,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| product2(e_3,e_3,e_2)
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f321,f4]) ).
fof(f324,definition,
( spl0_17
<=> product2(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f326,plain,
( product2(e_3,e_3,e_2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f328,definition,
( spl0_18
<=> product1(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f330,plain,
( product1(e_1,e_2,e_2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f332,definition,
( spl0_19
<=> product1(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f334,plain,
( product1(e_1,e_2,e_1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f335,plain,
( spl0_17
| spl0_18
| spl0_19
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f322,f306,f332,f328,f324]) ).
fof(f348,plain,
( equalish(e_2,e_3)
| ~ spl0_17 ),
inference(resolution,[],[f326,f30]) ).
fof(f350,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f348,f9]) ).
fof(f351,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f350]) ).
fof(f378,plain,
( equalish(e_1,e_2)
| ~ spl0_18 ),
inference(resolution,[],[f330,f28]) ).
fof(f387,plain,
( $false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f378,f6]) ).
fof(f388,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f415,plain,
( equalish(e_2,e_1)
| ~ spl0_19 ),
inference(resolution,[],[f334,f27]) ).
fof(f422,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f415,f8]) ).
fof(f423,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[],[f422]) ).
cnf(s16,plain,
spl0_16,
inference(sat_conversion,[],[f311]) ).
cnf(s17,plain,
( ~ spl0_16
| spl0_17
| spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f335]) ).
cnf(s18,plain,
~ spl0_17,
inference(sat_conversion,[],[f351]) ).
cnf(s20,plain,
~ spl0_18,
inference(sat_conversion,[],[f388]) ).
cnf(s21,plain,
~ spl0_19,
inference(sat_conversion,[],[f423]) ).
cnf(s22,plain,
~ spl0_16,
inference(rat,[],[s17,s21,s20,s18]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s16,s22]) ).
fof(f424,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:23:30 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.47 % (1392912)Will run a generic schedule for satisfiability detection.
% 0.11/0.47 % (1392920)dis+10_1_sil=32000:sp=arity:random_seed=3653546558:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.47 % (1392918)% WARNING: option uhcvi not known.
% 0.11/0.47 % (1392920) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1392912-1392920"...
% 0.11/0.47 % (1392920)...printing done.
% 0.11/0.47 % (1392921)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3771028127:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.47 % (1392922)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3175740579:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.47 % (1392919)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2467576853:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.47 % (1392923)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2274938936:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.47 % (1392920)Refutation found. Thanks to Tanya!
% 0.11/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.47 % (1392920)------------------------------
% 0.11/0.47 % (1392920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.47 % (1392920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.47 % (1392920)CaDiCaL version: 2.1.3
% 0.11/0.47 % (1392920)Termination reason: Refutation
% 0.11/0.47 % (1392920)Time elapsed: 0.004 s
% 0.11/0.47 % (1392920)Peak memory usage: 12 MB
% 0.11/0.47 % (1392920)Instructions burned: 10 (million)
% 0.11/0.47 % (1392912)Success in time 0.039 s
% 0.11/0.47 % Vampire exiting
%------------------------------------------------------------------------------