%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP040-4 : 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 : n001.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 10:16:29 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 63 ( 23 unt; 4 def)
% Number of atoms : 122 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 104 ( 45 ~; 55 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity1) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| subgroup_member(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
fof(f11,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X2)
| ~ product(X0,X1,X2)
| X1 = X3 ),
inference(reorient_equations,[],[f12]) ).
fof(f16,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(f17,axiom,
! [X0,X1] :
( product(X0,element_in_O2(X0,X1),X1)
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
fof(f18,axiom,
~ subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_in_subgroup) ).
fof(f19,axiom,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f20,axiom,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_in_subgroup) ).
fof(f21,axiom,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f22,axiom,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f23,negated_conjecture,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
fof(f24,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(superposition,[],[f3,f23]) ).
fof(f26,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) ),
inference(superposition,[],[f11,f23]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(X1)
| subgroup_member(X2) ),
inference(superposition,[],[f9,f23]) ).
fof(f62,plain,
! [X0] :
( ~ product(a,X0,d)
| c = X0 ),
inference(resolution,[],[f13,f22]) ).
fof(f63,plain,
! [X0] :
( ~ product(b,X0,c)
| inverse(a) = X0 ),
inference(resolution,[],[f13,f21]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f7,f1]) ).
fof(f98,plain,
! [X0,X1] :
( subgroup_member(multiply(X1,X0))
| ~ subgroup_member(X1)
| ~ subgroup_member(inverse(X0)) ),
inference(resolution,[],[f46,f5]) ).
fof(f122,plain,
( c = element_in_O2(a,d)
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[],[f62,f17]) ).
fof(f123,plain,
( c = element_in_O2(a,d)
| subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f122,f20]) ).
fof(f124,plain,
c = element_in_O2(a,d),
inference(forward_subsumption_resolution,[],[f123,f18]) ).
fof(f296,plain,
! [X2,X0,X1] :
( ~ product(inverse(X0),X1,X2)
| product(X0,X2,X1) ),
inference(resolution,[],[f80,f24]) ).
fof(f359,plain,
! [X0,X1] : product(X0,multiply(inverse(X0),X1),X1),
inference(resolution,[],[f296,f5]) ).
fof(f392,plain,
inverse(a) = multiply(inverse(b),c),
inference(resolution,[],[f359,f63]) ).
fof(f443,definition,
( spl0_4
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f444,plain,
( subgroup_member(inverse(a))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
( ~ subgroup_member(inverse(a))
| spl0_4 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f447,definition,
( spl0_5
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f448,plain,
( ~ subgroup_member(c)
| spl0_5 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f498,plain,
( subgroup_member(a)
| ~ spl0_4 ),
inference(resolution,[],[f444,f26]) ).
fof(f499,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f498,f18]) ).
fof(f500,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f499]) ).
fof(f541,plain,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[],[f98,f392]) ).
fof(f543,plain,
( ~ subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c))
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f541,f445]) ).
fof(f545,definition,
( spl0_9
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f547,plain,
( ~ subgroup_member(inverse(c))
| spl0_9 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f549,definition,
( spl0_10
<=> subgroup_member(inverse(b)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f551,plain,
( ~ subgroup_member(inverse(b))
| spl0_10 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f552,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f543,f443,f549,f545]) ).
fof(f610,plain,
( ~ subgroup_member(c)
| spl0_9 ),
inference(resolution,[],[f547,f11]) ).
fof(f621,plain,
( ~ subgroup_member(b)
| spl0_10 ),
inference(resolution,[],[f551,f11]) ).
fof(f622,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f621,f19]) ).
fof(f623,plain,
spl0_10,
inference(avatar_contradiction_clause,[],[f622]) ).
fof(f624,plain,
( ~ spl0_5
| spl0_9 ),
inference(avatar_split_clause,[],[f610,f545,f447]) ).
fof(f664,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a) ),
inference(superposition,[],[f16,f124]) ).
fof(f665,plain,
( subgroup_member(d)
| subgroup_member(a)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f664,f448]) ).
fof(f666,plain,
( subgroup_member(a)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f665,f20]) ).
fof(f667,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f666,f18]) ).
fof(f668,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f667]) ).
cnf(s4,plain,
~ spl0_4,
inference(sat_conversion,[],[f500]) ).
cnf(s7,plain,
( spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f552]) ).
cnf(s9,plain,
spl0_10,
inference(sat_conversion,[],[f623]) ).
cnf(s10,plain,
( ~ spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f624]) ).
cnf(s11,plain,
spl0_5,
inference(sat_conversion,[],[f668]) ).
cnf(s12,plain,
spl0_9,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
spl0_4,
inference(rat,[],[s7,s9,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s4,s13]) ).
fof(f669,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n001.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
% 0.11/0.39 % DateTime : Sun Sep 27 09:22:16 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
% 0.18/0.48 % (3284631)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (3284640)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=407354159:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (3284637)% WARNING: option uhcvi not known.
% 0.18/0.48 % (3284636)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1551532960_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (3284637)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=405938874:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (3284638)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=556640966:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (3284641)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=499016916:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (3284639)dis+10_1_sil=32000:sp=arity:random_seed=1285686055:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (3284642)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1988822893:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % TRYING [4]
% 0.18/0.48 % TRYING [5]
% 0.18/0.48 % (3284639) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3284631-3284639"...
% 0.18/0.48 % (3284639)...printing done.
% 0.18/0.48 % (3284639)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (3284639)------------------------------
% 0.18/0.48 % (3284639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (3284639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (3284639)CaDiCaL version: 2.1.3
% 0.18/0.48 % (3284639)Termination reason: Refutation
% 0.18/0.48 % (3284639)Time elapsed: 0.017 s
% 0.18/0.48 % (3284639)Peak memory usage: 12 MB
% 0.18/0.48 % (3284639)Instructions burned: 22 (million)
% 0.18/0.48 % (3284631)Success in time 0.05 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------