%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP039-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 10:12:13 AM UTC 2026
% Result : Unsatisfiable 3.42s 1.38s
% Output : Refutation 3.42s
% 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/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/benchmark/theBenchmark.p',closure_of_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f11,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(f12,axiom,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(X0)
| multiply(X0,element_in_O2(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f13,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_O2) ).
fof(f14,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f15,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f16,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f17,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(equality_resolution,[],[f6]) ).
fof(f29,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(superposition,[],[f17,f14]) ).
fof(f30,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[],[f17,f15]) ).
fof(f31,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f30,f16]) ).
fof(f32,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_subsumption_resolution,[],[f29,f13]) ).
fof(f34,definition,
( spl0_1
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f35,plain,
( subgroup_member(a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( ~ subgroup_member(a)
| spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f38,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,[],[f38]) ).
fof(f41,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f31,f38,f34]) ).
fof(f43,definition,
( spl0_3
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f45,plain,
( ~ subgroup_member(inverse(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f32,f38,f43]) ).
fof(f51,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f52,plain,
! [X0] : multiply(b,multiply(inverse(a),X0)) = multiply(c,X0),
inference(superposition,[],[f4,f14]) ).
fof(f59,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f51,f1]) ).
fof(f63,plain,
! [X0] :
( subgroup_member(X0)
| d = multiply(X0,element_in_O2(X0,d)) ),
inference(resolution,[],[f12,f16]) ).
fof(f68,plain,
( ~ subgroup_member(a)
| spl0_3 ),
inference(resolution,[],[f45,f5]) ).
fof(f91,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[],[f52,f3]) ).
fof(f100,plain,
b = multiply(c,a),
inference(forward_demodulation,[],[f91,f7]) ).
fof(f114,plain,
c = multiply(inverse(a),d),
inference(superposition,[],[f59,f15]) ).
fof(f117,plain,
a = multiply(inverse(c),b),
inference(superposition,[],[f59,f100]) ).
fof(f162,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[],[f17,f117]) ).
fof(f163,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f162,f36]) ).
fof(f165,plain,
( ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f163,f13]) ).
fof(f247,plain,
( ~ subgroup_member(c)
| spl0_1 ),
inference(resolution,[],[f165,f5]) ).
fof(f253,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f247,f34,f38]) ).
fof(f320,plain,
( $false
| ~ spl0_1
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f68,f35]) ).
fof(f321,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f320]) ).
fof(f334,plain,
( d = multiply(a,element_in_O2(a,d))
| spl0_1 ),
inference(resolution,[],[f36,f63]) ).
fof(f442,plain,
( element_in_O2(a,d) = multiply(inverse(a),d)
| spl0_1 ),
inference(superposition,[],[f59,f334]) ).
fof(f445,plain,
( c = element_in_O2(a,d)
| spl0_1 ),
inference(forward_demodulation,[],[f442,f114]) ).
fof(f525,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a)
| spl0_1 ),
inference(superposition,[],[f11,f445]) ).
fof(f526,plain,
( subgroup_member(d)
| subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f525,f40]) ).
fof(f529,plain,
( subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f526,f16]) ).
fof(f530,plain,
( $false
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f529,f36]) ).
fof(f531,plain,
( spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f530]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f253]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f321]) ).
cnf(s16,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f531]) ).
cnf(s17,plain,
spl0_1,
inference(rat,[],[s3,s16]) ).
cnf(s18,plain,
spl0_3,
inference(rat,[],[s6,s17]) ).
cnf(s19,plain,
~ spl0_2,
inference(rat,[],[s1,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s2,s18,s19]) ).
fof(f532,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n010.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 09:16:17 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/1.38 % (679121)Input is clausal, will run a generic CNF schedule.
% 3.42/1.38 % (679127)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=560126795:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.42/1.38 % (679128)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=672444309:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.42/1.38 % (679126)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1818087911:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.42/1.38 % (679131)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2485390121:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.42/1.38 % (679129)lrs+10_1_sil=8000:sp=occurrence:random_seed=3332832925:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.42/1.38 % (679130)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=833216743:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.42/1.38 % (679132)dis-21_1_sil=8000:lcm=predicate:random_seed=1643759685:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.42/1.38 % (679132)Refutation not found, incomplete strategy
% 3.42/1.38 % (679132)------------------------------
% 3.42/1.38 % (679132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.38 % (679132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.38 % (679132)CaDiCaL version: 2.1.3
% 3.42/1.38 % (679132)Termination reason: Refutation not found, incomplete strategy
% 3.42/1.38 % (679132)Time elapsed: 0.001 s
% 3.42/1.38 % (679132)Peak memory usage: 88 MB
% 3.42/1.38 % (679129)First to succeed.
% 3.42/1.38 % (679129)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-679121"
% 3.42/1.38 % (679131)Also succeeded, but the first one will report.
% 3.42/1.38 % (679130)Instruction limit reached!
% 3.42/1.38 % (679130)------------------------------
% 3.42/1.38 % (679130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.38 % (679130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.38 % (679130)CaDiCaL version: 2.1.3
% 3.42/1.38 % (679130)Termination reason: Instruction limit
% 3.42/1.38 % (679130)Termination phase: Saturation
% 3.42/1.38 % (679130)Time elapsed: 0.073 s
% 3.42/1.38 % (679130)Peak memory usage: 89 MB
% 3.42/1.38 % (679130)Instructions burned: 115 (million)
% 3.42/1.38 % (679140)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3688691998:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.42/1.38 % (679132)------------------------------
% 3.42/1.38 % (679132)------------------------------
% 3.42/1.38 % (679129)Refutation found. Thanks to Tanya!
% 3.42/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.42/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.38 % (679129)------------------------------
% 3.42/1.38 % (679129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.38 % (679129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.38 % (679129)CaDiCaL version: 2.1.3
% 3.42/1.38 % (679129)Termination reason: Refutation
% 3.42/1.38 % (679129)Time elapsed: 0.013 s
% 3.42/1.38 % (679129)Peak memory usage: 89 MB
% 3.42/1.38 % (679129)Instructions burned: 16 (million)
% 3.42/1.38 % (679129)------------------------------
% 3.42/1.38 % (679129)------------------------------
% 3.42/1.38 % (679121)Success in time 0.418 s
% 3.42/1.38 % Vampire exiting
%------------------------------------------------------------------------------