%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:12:39 AM UTC 2026
% Result : Unsatisfiable 3.56s 1.39s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 15 unt; 2 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 117 ( 48 ~; 67 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f12,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f15,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f16,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X2)
| ~ product(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f20,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f22,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X5,X4,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X0,X1,X2)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_2) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X2,X1)
| ~ product(X0,X2,X3)
| ~ product(X0,X0,X1)
| equalish(X2,X0) ),
inference(resolution,[],[f20,f22]) ).
fof(f29,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f18,f20]) ).
fof(f30,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f19,f20]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ product(X2,X2,e_3)
| product(X1,X0,e_1)
| product(X1,X0,e_2)
| ~ group_element(X1)
| ~ product(X2,X0,X1)
| ~ group_element(X0)
| equalish(X0,X2) ),
inference(resolution,[],[f16,f23]) ).
fof(f43,plain,
! [X0,X1] :
( ~ product(e_3,X1,X0)
| product(X0,X1,e_2)
| ~ group_element(X0)
| product(X0,X1,e_1)
| ~ group_element(X1)
| equalish(X1,e_3) ),
inference(resolution,[],[f37,f20]) ).
fof(f52,plain,
! [X0] :
( product(e_3,X0,e_2)
| ~ group_element(e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f43,f16]) ).
fof(f53,plain,
! [X0] :
( product(e_3,X0,e_2)
| ~ group_element(e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3) ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f55,plain,
! [X0] :
( product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3) ),
inference(forward_subsumption_resolution,[],[f53,f9]) ).
fof(f105,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3) ),
inference(resolution,[],[f30,f55]) ).
fof(f109,plain,
( product(e_3,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f105,f15]) ).
fof(f111,plain,
( product(e_3,e_2,e_1)
| equalish(e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f109,f8]) ).
fof(f112,plain,
product(e_3,e_2,e_1),
inference(forward_subsumption_resolution,[],[f111,f13]) ).
fof(f116,plain,
( product(e_1,e_2,e_2)
| ~ group_element(e_1)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3) ),
inference(resolution,[],[f112,f43]) ).
fof(f126,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f116,f7]) ).
fof(f128,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f126,f8]) ).
fof(f129,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution,[],[f128,f13]) ).
fof(f131,definition,
( spl0_3
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f133,plain,
( product(e_1,e_2,e_1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f135,definition,
( spl0_4
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f137,plain,
( product(e_1,e_2,e_2)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f129,f135,f131]) ).
fof(f154,plain,
( equalish(e_1,e_2)
| ~ spl0_4 ),
inference(resolution,[],[f137,f30]) ).
fof(f155,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f154,f10]) ).
fof(f156,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f161,plain,
( equalish(e_2,e_1)
| ~ spl0_3 ),
inference(resolution,[],[f133,f29]) ).
fof(f170,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f161,f12]) ).
fof(f171,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f170]) ).
cnf(s3,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f138]) ).
cnf(s4,plain,
~ spl0_4,
inference(sat_conversion,[],[f156]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f171]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s4,s5]) ).
fof(f172,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:19:52 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 3.56/1.39 % (3247838)Input is clausal, will run a generic CNF schedule.
% 3.56/1.39 % (3247922)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3115871878:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.56/1.39 % (3247922)Refutation not found, incomplete strategy
% 3.56/1.39 % (3247922)------------------------------
% 3.56/1.39 % (3247922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.39 % (3247922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.39 % (3247922)CaDiCaL version: 2.1.3
% 3.56/1.39 % (3247922)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.39 % (3247922)Time elapsed: 0.001 s
% 3.56/1.39 % (3247922)Peak memory usage: 87 MB
% 3.56/1.39 % (3247922)Instructions burned: 1 (million)
% 3.56/1.39 % (3247920)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4250528806:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.56/1.39 % (3247918)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=2907432320:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.56/1.39 % (3247921)lrs+10_1_sil=8000:sp=occurrence:random_seed=2771087815:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.56/1.39 % (3247921)First to succeed.
% 3.56/1.39 % (3247921)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3247838"
% 3.56/1.39 % (3247919)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=164770687:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.56/1.39 % (3247923)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1499076792:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.56/1.39 % (3247924)dis-21_1_sil=8000:lcm=predicate:random_seed=2490344360: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)
% 3.56/1.39 % (3247923)Also succeeded, but the first one will report.
% 3.56/1.39 % (3247924)Instruction limit reached!
% 3.56/1.39 % (3247924)------------------------------
% 3.56/1.39 % (3247924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.39 % (3247924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.39 % (3247924)CaDiCaL version: 2.1.3
% 3.56/1.39 % (3247924)Termination reason: Instruction limit
% 3.56/1.39 % (3247924)Termination phase: Saturation
% 3.56/1.39 % (3247924)Time elapsed: 0.068 s
% 3.56/1.39 % (3247924)Peak memory usage: 88 MB
% 3.56/1.39 % (3247924)Instructions burned: 118 (million)
% 3.56/1.39 % (3247922)------------------------------
% 3.56/1.39 % (3247922)------------------------------
% 3.56/1.39 % (3247964)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1882753639: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)
% 3.56/1.39 % (3247964)Refutation not found, incomplete strategy
% 3.56/1.39 % (3247964)------------------------------
% 3.56/1.39 % (3247964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.39 % (3247964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.39 % (3247964)CaDiCaL version: 2.1.3
% 3.56/1.39 % (3247964)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.39 % (3247964)Time elapsed: 0.001 s
% 3.56/1.39 % (3247964)Peak memory usage: 87 MB
% 3.56/1.39 % (3247964)Instructions burned: 2 (million)
% 3.56/1.39 % (3247963)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=1040744757:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.56/1.39 % (3247963)Also succeeded, but the first one will report.
% 3.56/1.39 % (3247921)Refutation found. Thanks to Tanya!
% 3.56/1.39 % SZS status Unsatisfiable for theBenchmark
% 3.56/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.39 % (3247921)------------------------------
% 3.56/1.39 % (3247921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.39 % (3247921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.39 % (3247921)CaDiCaL version: 2.1.3
% 3.56/1.39 % (3247921)Termination reason: Refutation
% 3.56/1.39 % (3247921)Time elapsed: 0.006 s
% 3.56/1.39 % (3247921)Peak memory usage: 89 MB
% 3.56/1.39 % (3247921)Instructions burned: 7 (million)
% 3.56/1.39 % (3247921)------------------------------
% 3.56/1.39 % (3247921)------------------------------
% 3.56/1.39 % (3247838)Success in time 0.443 s
% 3.56/1.39 % Vampire exiting
%------------------------------------------------------------------------------