%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n005.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 3.86s 1.56s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 49 ( 18 unt; 2 def)
% Number of atoms : 99 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 91 ( 41 ~; 48 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
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/theBenchmark.p',associativity1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
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/theBenchmark.p',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(f41,plain,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(X1)
| subgroup_member(X2) ),
inference(superposition,[],[f9,f23]) ).
fof(f59,plain,
! [X0] :
( ~ product(a,X0,d)
| c = X0 ),
inference(resolution,[],[f13,f22]) ).
fof(f62,plain,
( c = element_in_O2(a,d)
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[],[f59,f17]) ).
fof(f63,plain,
( c = element_in_O2(a,d)
| subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f62,f20]) ).
fof(f64,plain,
c = element_in_O2(a,d),
inference(forward_subsumption_resolution,[],[f63,f18]) ).
fof(f73,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a) ),
inference(superposition,[],[f16,f64]) ).
fof(f74,plain,
( subgroup_member(c)
| subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f73,f20]) ).
fof(f75,plain,
subgroup_member(c),
inference(forward_subsumption_resolution,[],[f74,f18]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f7,f1]) ).
fof(f87,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X0,identity,X3)
| product(X2,X1,X3) ),
inference(resolution,[],[f8,f3]) ).
fof(f187,plain,
! [X2,X0,X1] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f79,f3]) ).
fof(f285,plain,
! [X0] :
( ~ product(b,identity,X0)
| product(c,a,X0) ),
inference(resolution,[],[f87,f21]) ).
fof(f289,plain,
product(c,a,b),
inference(resolution,[],[f285,f2]) ).
fof(f637,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(inverse(X0))
| subgroup_member(X1) ),
inference(resolution,[],[f187,f41]) ).
fof(f676,plain,
( ~ subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c))
| subgroup_member(a) ),
inference(resolution,[],[f637,f289]) ).
fof(f678,plain,
( ~ subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c)) ),
inference(forward_subsumption_resolution,[],[f676,f18]) ).
fof(f687,definition,
( spl0_29
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f689,plain,
( ~ subgroup_member(inverse(c))
| spl0_29 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f691,definition,
( spl0_30
<=> subgroup_member(inverse(b)) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f693,plain,
( ~ subgroup_member(inverse(b))
| spl0_30 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f694,plain,
( ~ spl0_29
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f678,f691,f687]) ).
fof(f726,plain,
( ~ subgroup_member(c)
| spl0_29 ),
inference(resolution,[],[f689,f11]) ).
fof(f730,plain,
( $false
| spl0_29 ),
inference(forward_subsumption_resolution,[],[f726,f75]) ).
fof(f731,plain,
spl0_29,
inference(avatar_contradiction_clause,[],[f730]) ).
fof(f791,plain,
( ~ subgroup_member(b)
| spl0_30 ),
inference(resolution,[],[f693,f11]) ).
fof(f795,plain,
( $false
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f791,f19]) ).
fof(f796,plain,
spl0_30,
inference(avatar_contradiction_clause,[],[f795]) ).
cnf(s27,plain,
( ~ spl0_29
| ~ spl0_30 ),
inference(sat_conversion,[],[f694]) ).
cnf(s32,plain,
spl0_29,
inference(sat_conversion,[],[f731]) ).
cnf(s35,plain,
spl0_30,
inference(sat_conversion,[],[f796]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s27,s35,s32]) ).
fof(f797,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 THM
% 0.11/0.40 % Computer : n005.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 09:16:17 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.86/1.56 % (3718340)Input is clausal, will run a generic CNF schedule.
% 3.86/1.56 % (3718464)dis-21_1_sil=8000:lcm=predicate:random_seed=379939933: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)
% 3.86/1.56 % (3718464)Instruction limit reached!
% 3.86/1.56 % (3718464)------------------------------
% 3.86/1.56 % (3718464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.56 % (3718464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.56 % (3718464)CaDiCaL version: 2.1.3
% 3.86/1.56 % (3718464)Termination reason: Instruction limit
% 3.86/1.56 % (3718464)Termination phase: Saturation
% 3.86/1.56 % (3718464)Time elapsed: 0.030 s
% 3.86/1.56 % (3718464)Peak memory usage: 88 MB
% 3.86/1.56 % (3718464)Instructions burned: 121 (million)
% 3.86/1.56 % (3718458)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=59634335:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.86/1.56 % (3718461)lrs+10_1_sil=8000:sp=occurrence:random_seed=2173316937:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.86/1.56 % (3718459)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1124507916:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.86/1.56 % (3718463)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=365859475:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.86/1.56 % (3718462)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3020198226:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.86/1.56 % (3718460)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1115419720:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.86/1.56 % (3718461)First to succeed.
% 3.86/1.56 % (3718461)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3718340"
% 3.86/1.56 % (3718463)Also succeeded, but the first one will report.
% 3.86/1.56 % (3718462)Instruction limit reached!
% 3.86/1.56 % (3718462)------------------------------
% 3.86/1.56 % (3718462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.56 % (3718462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.56 % (3718462)CaDiCaL version: 2.1.3
% 3.86/1.56 % (3718462)Termination reason: Instruction limit
% 3.86/1.56 % (3718462)Termination phase: Saturation
% 3.86/1.56 % (3718462)Time elapsed: 0.072 s
% 3.86/1.56 % (3718462)Peak memory usage: 88 MB
% 3.86/1.56 % (3718462)Instructions burned: 115 (million)
% 3.86/1.56 % (3718466)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=3528898094:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.86/1.56 % (3718466)Also succeeded, but the first one will report.
% 3.86/1.56 % (3718473)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1458235516:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.86/1.56 % (3718461)Refutation found. Thanks to Tanya!
% 3.86/1.56 % SZS status Unsatisfiable for theBenchmark
% 3.86/1.56 % SZS output start Proof for theBenchmark
% See solution above
% 3.86/1.56 % (3718461)------------------------------
% 3.86/1.56 % (3718461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.56 % (3718461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.56 % (3718461)CaDiCaL version: 2.1.3
% 3.86/1.56 % (3718461)Termination reason: Refutation
% 3.86/1.56 % (3718461)Time elapsed: 0.018 s
% 3.86/1.56 % (3718461)Peak memory usage: 89 MB
% 3.86/1.56 % (3718461)Instructions burned: 24 (million)
% 3.86/1.56 % (3718461)------------------------------
% 3.86/1.56 % (3718461)------------------------------
% 3.86/1.56 % (3718340)Success in time 0.471 s
% 3.86/1.56 % Vampire exiting
%------------------------------------------------------------------------------