%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP039-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 73 ( 20 unt; 4 def)
% Number of atoms : 162 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 157 ( 68 ~; 85 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 81 ( 0 sgn 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
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/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ product(X0,inverse(X1),X2)
| subgroup_member(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| X3 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f11,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X2)
| ~ product(X0,X1,X2)
| X1 = X3 ),
inference(reorient_equations,[],[f10]) ).
fof(f14,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
fof(f15,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
fof(f16,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subgroup_member_inverse_are_in_subgroup) ).
fof(f17,axiom,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f18,axiom,
! [X0,X1] :
( product(X0,element_in_O2(X0,X1),X1)
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f19,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f20,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f21,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f22,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[],[f6,f5]) ).
fof(f29,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[],[f6,f2]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ subgroup_member(X0)
| ~ product(X0,inverse(inverse(X1)),X2)
| subgroup_member(X2)
| ~ subgroup_member(X1) ),
inference(resolution,[],[f9,f16]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(element_in_O2(X1,X2)),X3)
| ~ subgroup_member(X0)
| subgroup_member(X3)
| subgroup_member(X2)
| subgroup_member(X1) ),
inference(resolution,[],[f9,f17]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| subgroup_member(X2)
| ~ product(X0,X1,X2) ),
inference(forward_demodulation,[],[f37,f14]) ).
fof(f51,plain,
! [X0] :
( ~ product(a,X0,d)
| c = X0 ),
inference(resolution,[],[f11,f21]) ).
fof(f61,plain,
( c = element_in_O2(a,d)
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[],[f51,f18]) ).
fof(f62,plain,
( c = element_in_O2(a,d)
| subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f61,f22]) ).
fof(f64,definition,
( spl0_1
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f66,plain,
( subgroup_member(a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_2
<=> c = element_in_O2(a,d) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f70,plain,
( c = element_in_O2(a,d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f62,f68,f64]) ).
fof(f72,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X3,X0,X4)
| ~ product(X0,X1,X2)
| product(X3,X2,multiply(X4,X1)) ),
inference(resolution,[],[f7,f5]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f7,f1]) ).
fof(f88,plain,
( ! [X0,X1] :
( ~ product(X0,inverse(a),X1)
| ~ subgroup_member(X0)
| subgroup_member(X1) )
| ~ spl0_1 ),
inference(resolution,[],[f66,f9]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,c)
| ~ product(a,X0,X2)
| product(X2,X1,d) ),
inference(resolution,[],[f8,f21]) ).
fof(f114,plain,
! [X0] :
( ~ product(a,b,X0)
| product(X0,inverse(a),d) ),
inference(resolution,[],[f97,f20]) ).
fof(f231,plain,
! [X0,X1] :
( ~ product(X0,b,X1)
| subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[],[f40,f19]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(inverse(X0),X2,X1) ),
inference(resolution,[],[f76,f3]) ).
fof(f290,plain,
! [X0] :
( subgroup_member(multiply(X0,b))
| ~ subgroup_member(X0) ),
inference(resolution,[],[f231,f5]) ).
fof(f324,plain,
! [X0,X1] :
( ~ product(inverse(a),X0,X1)
| product(b,X1,multiply(c,X0)) ),
inference(resolution,[],[f72,f20]) ).
fof(f343,plain,
! [X0,X1] :
( ~ subgroup_member(identity)
| subgroup_member(inverse(element_in_O2(X0,X1)))
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(resolution,[],[f38,f1]) ).
fof(f346,plain,
! [X0,X1] :
( subgroup_member(inverse(element_in_O2(X0,X1)))
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(forward_subsumption_resolution,[],[f343,f15]) ).
fof(f357,plain,
product(multiply(a,b),inverse(a),d),
inference(resolution,[],[f114,f5]) ).
fof(f380,definition,
( spl0_7
<=> subgroup_member(multiply(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f381,plain,
( ~ subgroup_member(multiply(a,b))
| spl0_7 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f382,plain,
( subgroup_member(multiply(a,b))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f424,plain,
product(b,identity,multiply(c,a)),
inference(resolution,[],[f324,f3]) ).
fof(f468,plain,
b = multiply(c,a),
inference(resolution,[],[f424,f29]) ).
fof(f481,plain,
product(c,a,b),
inference(superposition,[],[f5,f468]) ).
fof(f630,plain,
product(inverse(c),b,a),
inference(resolution,[],[f242,f481]) ).
fof(f708,plain,
a = multiply(inverse(c),b),
inference(resolution,[],[f630,f28]) ).
fof(f780,definition,
( spl0_10
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f812,plain,
( subgroup_member(inverse(c))
| subgroup_member(d)
| subgroup_member(a)
| ~ spl0_2 ),
inference(superposition,[],[f346,f70]) ).
fof(f1097,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[],[f290,f708]) ).
fof(f1759,plain,
( ~ subgroup_member(multiply(a,b))
| subgroup_member(d)
| ~ spl0_1 ),
inference(resolution,[],[f88,f357]) ).
fof(f1762,plain,
( subgroup_member(d)
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1759,f382]) ).
fof(f1763,plain,
( $false
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1762,f22]) ).
fof(f1764,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1763]) ).
fof(f1868,plain,
( ~ subgroup_member(a)
| spl0_7 ),
inference(resolution,[],[f381,f290]) ).
fof(f1904,plain,
( subgroup_member(inverse(c))
| subgroup_member(a)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f812,f22]) ).
fof(f1905,plain,
( ~ spl0_10
| spl0_1 ),
inference(avatar_split_clause,[],[f1097,f64,f780]) ).
fof(f1951,plain,
( ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f1868,f380,f64]) ).
fof(f1968,plain,
( spl0_1
| spl0_10
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1904,f68,f780,f64]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f71]) ).
cnf(s10,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f1764]) ).
cnf(s45,plain,
( spl0_1
| ~ spl0_10 ),
inference(sat_conversion,[],[f1905]) ).
cnf(s55,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f1951]) ).
cnf(s59,plain,
( spl0_1
| ~ spl0_2
| spl0_10 ),
inference(sat_conversion,[],[f1968]) ).
cnf(s62,plain,
spl0_1,
inference(rat,[],[s59,s1,s45]) ).
cnf(s63,plain,
spl0_7,
inference(rat,[],[s55,s62]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s10,s63,s62]) ).
fof(f1975,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:15:47 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.16/0.52 % (538748)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (538755)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3696228312:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (538754)% WARNING: option uhcvi not known.
% 0.16/0.52 % (538758)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3107267162:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % (538753)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=312024922_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (538754)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2814929258:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (538756)dis+10_1_sil=32000:sp=arity:random_seed=1232378109:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (538757)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2609293873:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (538759)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2537788034:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % TRYING [4]
% 0.16/0.52 % TRYING [5]
% 0.16/0.52 % TRYING [6]
% 0.16/0.52 % (538754) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-538748-538754"...
% 0.16/0.52 % (538754)...printing done.
% 0.16/0.52 % (538754)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (538754)------------------------------
% 0.16/0.52 % (538754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (538754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (538754)CaDiCaL version: 2.1.3
% 0.16/0.52 % (538754)Termination reason: Refutation
% 0.16/0.52 % (538754)Time elapsed: 0.044 s
% 0.16/0.52 % (538754)Peak memory usage: 13 MB
% 0.16/0.52 % (538754)Instructions burned: 63 (million)
% 0.16/0.52 % (538748)Success in time 0.091 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------