%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 10:16:54 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 79 ( 12 unt; 8 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 217 ( 114 ~; 95 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 41 !; 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(f7,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f8,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(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,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(f13,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(f14,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_2)
| ~ product(X3,e_1,X1) ),
inference(resolution,[],[f6,f13]) ).
fof(f15,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,[],[f6,f12]) ).
fof(f22,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f10,f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f11,f7]) ).
fof(f25,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2) ),
inference(resolution,[],[f8,f4]) ).
fof(f26,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2) ),
inference(resolution,[],[f8,f5]) ).
fof(f29,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[],[f25,f4]) ).
fof(f30,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[],[f25,f5]) ).
fof(f32,definition,
( spl0_1
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f34,plain,
( product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f36,definition,
( spl0_2
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f38,plain,
( product(e_1,e_2,e_1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f30,f36,f32]) ).
fof(f41,definition,
( spl0_3
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f43,plain,
( product(e_1,e_1,e_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl0_4
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f47,plain,
( product(e_1,e_1,e_1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f29,f45,f41]) ).
fof(f49,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f38,f22]) ).
fof(f51,plain,
( ~ spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f49,f36,f45]) ).
fof(f52,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[],[f26,f4]) ).
fof(f53,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[],[f26,f5]) ).
fof(f55,definition,
( spl0_5
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f57,plain,
( product(e_2,e_2,e_2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f59,definition,
( spl0_6
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f61,plain,
( product(e_2,e_2,e_1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f53,f59,f55]) ).
fof(f64,definition,
( spl0_7
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f66,plain,
( product(e_2,e_1,e_2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_8
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f71,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f52,f68,f64]) ).
fof(f75,plain,
( ! [X0,X1] :
( ~ product(X0,e_2,e_2)
| ~ product(X1,e_1,e_1)
| ~ product(X1,X0,e_2) )
| ~ spl0_3 ),
inference(resolution,[],[f43,f14]) ).
fof(f79,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_5 ),
inference(resolution,[],[f57,f24]) ).
fof(f82,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_5 ),
inference(resolution,[],[f57,f22]) ).
fof(f85,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1)
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f57,f75]) ).
fof(f89,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f85,f57]) ).
fof(f90,plain,
( $false
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f82,f66]) ).
fof(f91,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f92,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f79,f55,f32]) ).
fof(f93,plain,
( ~ spl0_8
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f89,f55,f41,f68]) ).
fof(f94,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_6 ),
inference(resolution,[],[f61,f24]) ).
fof(f95,plain,
( ! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,e_2)
| ~ product(e_1,X1,e_1) )
| ~ spl0_6 ),
inference(resolution,[],[f61,f15]) ).
fof(f102,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f94,f38]) ).
fof(f103,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f102]) ).
fof(f104,plain,
( ! [X0] :
( ~ product(e_1,e_1,X0)
| ~ product(e_1,X0,e_1) )
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f34,f95]) ).
fof(f106,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f34,f22]) ).
fof(f109,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f106,f43]) ).
fof(f110,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f112,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f47,f104]) ).
fof(f120,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f112,f47]) ).
fof(f121,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f120]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f62]) ).
cnf(s5,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f71]) ).
cnf(s7,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f91]) ).
cnf(s8,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f92]) ).
cnf(s9,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f93]) ).
cnf(s11,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(sat_conversion,[],[f103]) ).
cnf(s12,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f110]) ).
cnf(s14,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f121]) ).
cnf(s15,plain,
~ spl0_2,
inference(rat,[],[s5,s9,s7,s2,s4,s3,s11]) ).
cnf(s16,plain,
spl0_1,
inference(rat,[],[s1,s15]) ).
cnf(s17,plain,
~ spl0_3,
inference(rat,[],[s12,s16]) ).
cnf(s18,plain,
~ spl0_5,
inference(rat,[],[s8,s16]) ).
cnf(s19,plain,
spl0_4,
inference(rat,[],[s2,s17]) ).
cnf(s20,plain,
spl0_6,
inference(rat,[],[s4,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s14,s16,s20,s19]) ).
fof(f122,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:31:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.11/0.46 % (2831324)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (2831333)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3338302980:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (2831333) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2831324-2831333"...
% 0.11/0.46 % (2831330)% WARNING: option uhcvi not known.
% 0.11/0.46 % (2831333)...printing done.
% 0.11/0.46 % (2831333)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (2831333)------------------------------
% 0.16/0.46 % (2831333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (2831333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (2831333)CaDiCaL version: 2.1.3
% 0.16/0.46 % (2831333)Termination reason: Refutation
% 0.16/0.46 % (2831333)Time elapsed: 0.002 s
% 0.16/0.46 % (2831333)Peak memory usage: 12 MB
% 0.16/0.46 % (2831333)Instructions burned: 5 (million)
% 0.16/0.46 % (2831324)Success in time 0.031 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------