%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:12:40 AM UTC 2026
% Result : Unsatisfiable 5.11s 1.86s
% Output : Refutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 55 ( 17 unt; 4 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 118 ( 60 ~; 54 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f7,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f10,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f11,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f12,axiom,
! [X0,X1] :
( product1(X0,X1,e_3)
| ~ group_element(X1)
| product1(X0,X1,e_1)
| product1(X0,X1,e_2)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f16,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( ~ product2(X0,X1,X2)
| ~ product2(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f21,axiom,
! [X0] : product2(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f22,negated_conjecture,
! [X2,X3,X0,X1] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
fof(f25,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[],[f15,f6]) ).
fof(f27,plain,
! [X0,X1] :
( ~ product1(X0,e_1,X1)
| ~ product1(X0,e_3,X1) ),
inference(resolution,[],[f7,f14]) ).
fof(f30,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[],[f18,f7]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4] :
( ~ product1(X4,X2,X0)
| equalish(X3,X1)
| ~ product2(X0,X1,X2)
| ~ product1(X3,X2,X4) ),
inference(resolution,[],[f19,f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ product1(X0,X2,X2)
| ~ product2(X2,X1,X2)
| equalish(X0,X1) ),
inference(resolution,[],[f35,f16]) ).
fof(f43,plain,
! [X0,X1] :
( ~ product2(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f38,f16]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ product1(X2,X0,X0)
| equalish(X0,X1)
| ~ product1(X1,X0,X2) ),
inference(resolution,[],[f43,f22]) ).
fof(f77,plain,
! [X0,X1] :
( ~ product1(X1,X0,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f47,f16]) ).
fof(f82,plain,
! [X0] :
( equalish(e_3,X0)
| ~ group_element(e_3)
| product1(X0,e_3,e_1)
| product1(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f77,f12]) ).
fof(f83,plain,
! [X0] :
( equalish(e_3,X0)
| product1(X0,e_3,e_1)
| product1(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[],[f82,f5]) ).
fof(f105,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| ~ group_element(e_1) ),
inference(resolution,[],[f83,f10]) ).
fof(f106,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| ~ group_element(e_2) ),
inference(resolution,[],[f83,f11]) ).
fof(f107,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f106,f4]) ).
fof(f108,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f105,f3]) ).
fof(f110,definition,
( spl0_1
<=> product1(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f112,plain,
( product1(e_2,e_3,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f114,definition,
( spl0_2
<=> product1(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f116,plain,
( product1(e_2,e_3,e_1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f107,f114,f110]) ).
fof(f119,definition,
( spl0_3
<=> product1(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f123,definition,
( spl0_4
<=> product1(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f126,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f108,f123,f119]) ).
fof(f149,plain,
~ product1(e_1,e_3,e_1),
inference(resolution,[],[f27,f16]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ product2(X0,X1,e_1)
| ~ product1(X2,e_3,X0)
| ~ product1(X1,e_3,X2) ),
inference(resolution,[],[f30,f22]) ).
fof(f171,plain,
! [X0] :
( ~ product1(X0,e_3,e_1)
| ~ product1(e_1,e_3,X0) ),
inference(resolution,[],[f167,f21]) ).
fof(f172,plain,
( ~ product1(e_1,e_3,e_2)
| ~ spl0_2 ),
inference(resolution,[],[f171,f116]) ).
fof(f177,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f149,f123]) ).
fof(f178,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f172,f114,f119]) ).
fof(f179,plain,
( ~ product1(e_1,e_3,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f112,f25]) ).
fof(f185,plain,
( ~ spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f179,f110,f119]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f117]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f126]) ).
cnf(s6,plain,
~ spl0_4,
inference(sat_conversion,[],[f177]) ).
cnf(s8,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f178]) ).
cnf(s11,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f185]) ).
cnf(s12,plain,
spl0_3,
inference(rat,[],[s2,s6]) ).
cnf(s13,plain,
~ spl0_1,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
~ spl0_2,
inference(rat,[],[s8,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s14,s13]) ).
fof(f186,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 % Computer : n010.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 27 09:20:33 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 5.11/1.86 % (685339)Input is clausal, will run a generic CNF schedule.
% 5.11/1.86 % (685360)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=2372915938:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.11/1.86 % (685365)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1541141996:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.11/1.86 % (685365)First to succeed.
% 5.11/1.86 % (685365)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-685339"
% 5.11/1.86 % (685364)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3667807727:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.11/1.86 % (685366)dis-21_1_sil=8000:lcm=predicate:random_seed=675352005: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)
% 5.11/1.86 % (685364)Also succeeded, but the first one will report.
% 5.11/1.86 % (685366)Also succeeded, but the first one will report.
% 5.11/1.86 % (685363)lrs+10_1_sil=8000:sp=occurrence:random_seed=1365911812:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.11/1.86 % (685362)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1299538096:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.11/1.86 % (685361)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2030739:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.11/1.86 % (685363)Also succeeded, but the first one will report.
% 5.11/1.86 % (685365)Refutation found. Thanks to Tanya!
% 5.11/1.86 % SZS status Unsatisfiable for theBenchmark
% 5.11/1.86 % SZS output start Proof for theBenchmark
% See solution above
% 5.11/1.86 % (685365)------------------------------
% 5.11/1.86 % (685365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.86 % (685365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.86 % (685365)CaDiCaL version: 2.1.3
% 5.11/1.86 % (685365)Termination reason: Refutation
% 5.11/1.86 % (685365)Time elapsed: 0.011 s
% 5.11/1.86 % (685365)Peak memory usage: 89 MB
% 5.11/1.86 % (685365)Instructions burned: 7 (million)
% 5.11/1.86 % (685365)------------------------------
% 5.11/1.86 % (685365)------------------------------
% 5.11/1.86 % (685339)Success in time 0.613 s
% 5.11/1.86 % Vampire exiting
%------------------------------------------------------------------------------