%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:16:28 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 21 unt; 3 def)
% Number of atoms : 117 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 93 ( 37 ~; 53 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-1.ax',closure_of_inverse) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| multiply(X0,X1) != X2
| subgroup_member(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f10,axiom,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f11,axiom,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| multiply(X0,element_in_O2(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
fof(f12,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
fof(f13,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f14,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f15,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f16,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(equality_resolution,[],[f6]) ).
fof(f28,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(superposition,[],[f16,f13]) ).
fof(f29,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[],[f16,f14]) ).
fof(f30,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f29,f15]) ).
fof(f31,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_subsumption_resolution,[],[f28,f12]) ).
fof(f35,definition,
( spl0_1
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f37,plain,
( ~ subgroup_member(a)
| spl0_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f39,definition,
( spl0_2
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f40,plain,
( subgroup_member(c)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( ~ subgroup_member(c)
| spl0_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f30,f39,f35]) ).
fof(f44,definition,
( spl0_3
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f46,plain,
( ~ subgroup_member(inverse(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f31,f39,f44]) ).
fof(f61,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f62,plain,
! [X0] : multiply(b,multiply(inverse(a),X0)) = multiply(c,X0),
inference(superposition,[],[f4,f13]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f61,f1]) ).
fof(f73,plain,
( ~ subgroup_member(a)
| spl0_3 ),
inference(resolution,[],[f46,f5]) ).
fof(f77,plain,
! [X0] :
( subgroup_member(X0)
| d = multiply(X0,element_in_O2(X0,d)) ),
inference(resolution,[],[f11,f15]) ).
fof(f102,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f73,f44,f35]) ).
fof(f120,plain,
( d = multiply(a,element_in_O2(a,d))
| spl0_1 ),
inference(resolution,[],[f77,f37]) ).
fof(f125,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[],[f62,f3]) ).
fof(f134,plain,
b = multiply(c,a),
inference(forward_demodulation,[],[f125,f7]) ).
fof(f150,plain,
c = multiply(inverse(a),d),
inference(superposition,[],[f69,f14]) ).
fof(f152,plain,
a = multiply(inverse(c),b),
inference(superposition,[],[f69,f134]) ).
fof(f191,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[],[f16,f152]) ).
fof(f192,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f191,f37]) ).
fof(f194,plain,
( ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f192,f12]) ).
fof(f199,plain,
( ~ subgroup_member(c)
| spl0_1 ),
inference(resolution,[],[f194,f5]) ).
fof(f354,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f199,f40]) ).
fof(f355,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f364,plain,
( element_in_O2(a,d) = multiply(inverse(a),d)
| spl0_1 ),
inference(superposition,[],[f69,f120]) ).
fof(f367,plain,
( c = element_in_O2(a,d)
| spl0_1 ),
inference(forward_demodulation,[],[f364,f150]) ).
fof(f418,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a)
| spl0_1 ),
inference(superposition,[],[f10,f367]) ).
fof(f419,plain,
( subgroup_member(d)
| subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f418,f41]) ).
fof(f420,plain,
( subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f419,f15]) ).
fof(f421,plain,
( $false
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f420,f37]) ).
fof(f422,plain,
( spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f421]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f102]) ).
cnf(s10,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f355]) ).
cnf(s13,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f422]) ).
cnf(s15,plain,
spl0_1,
inference(rat,[],[s10,s13]) ).
cnf(s16,plain,
spl0_3,
inference(rat,[],[s6,s15]) ).
cnf(s17,plain,
~ spl0_2,
inference(rat,[],[s1,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s2,s16,s17]) ).
fof(f423,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/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 09:19:15 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (1385754)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (1385763)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=897824813:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (1385760)% WARNING: option uhcvi not known.
% 0.17/0.48 % (1385763) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1385754-1385763"...
% 0.17/0.48 % (1385763)...printing done.
% 0.17/0.48 % (1385763)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (1385763)------------------------------
% 0.17/0.48 % (1385763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1385763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1385763)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1385763)Termination reason: Refutation
% 0.17/0.48 % (1385763)Time elapsed: 0.006 s
% 0.17/0.48 % (1385763)Peak memory usage: 12 MB
% 0.17/0.48 % (1385763)Instructions burned: 14 (million)
% 0.17/0.48 % (1385754)Success in time 0.047 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------