%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 10:16:44 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 26 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 33 ( 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(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f14,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
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] :
( 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(f18,axiom,
! [X2,X3,X0,X1] :
( ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f20,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f26,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2)
| product2(X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
fof(f35,plain,
! [X0,X1] :
( ~ product1(X0,X1,X1)
| product2(X1,X0,X1) ),
inference(resolution,[],[f20,f26]) ).
fof(f58,plain,
! [X0,X1] :
( ~ product1(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f18,f20]) ).
fof(f78,plain,
! [X0] : product2(X0,X0,X0),
inference(resolution,[],[f35,f20]) ).
fof(f89,plain,
! [X0,X1] :
( ~ product2(X0,X0,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f78,f22]) ).
fof(f96,plain,
! [X0,X1] :
( ~ product2(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f23,f78]) ).
fof(f127,plain,
! [X0] :
( ~ group_element(e_3)
| product1(X0,e_3,e_1)
| product1(X0,e_3,e_2)
| ~ group_element(X0)
| product2(e_3,X0,e_3) ),
inference(resolution,[],[f16,f35]) ).
fof(f132,plain,
! [X0] :
( product2(e_3,X0,e_3)
| product1(X0,e_3,e_2)
| ~ group_element(X0)
| product1(X0,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f127,f9]) ).
fof(f152,plain,
! [X0] :
( product1(X0,e_3,e_2)
| ~ group_element(X0)
| product1(X0,e_3,e_1)
| equalish(X0,e_3) ),
inference(resolution,[],[f132,f96]) ).
fof(f197,plain,
( ~ group_element(e_2)
| product1(e_2,e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[],[f152,f58]) ).
fof(f199,plain,
( product1(e_2,e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f197,f8]) ).
fof(f200,plain,
( product1(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f199,f13]) ).
fof(f201,plain,
product1(e_2,e_3,e_1),
inference(forward_subsumption_resolution,[],[f200,f15]) ).
fof(f209,plain,
! [X0] :
( ~ product1(X0,e_3,e_2)
| product2(e_1,X0,e_3) ),
inference(resolution,[],[f201,f26]) ).
fof(f252,plain,
! [X0] :
( product2(e_1,X0,e_3)
| ~ group_element(X0)
| product1(X0,e_3,e_1)
| equalish(X0,e_3) ),
inference(resolution,[],[f209,f152]) ).
fof(f281,plain,
( ~ group_element(e_1)
| product1(e_1,e_3,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_1) ),
inference(resolution,[],[f252,f89]) ).
fof(f282,plain,
( product1(e_1,e_3,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f281,f7]) ).
fof(f283,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f282,f58]) ).
fof(f284,plain,
equalish(e_3,e_1),
inference(forward_subsumption_resolution,[],[f283,f11]) ).
fof(f285,plain,
$false,
inference(forward_subsumption_resolution,[],[f284,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n002.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 09:23:07 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 % (3280063)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3280070)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=525579356:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3280070) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3280063-3280070"...
% 0.17/0.47 % (3280070)...printing done.
% 0.17/0.47 % (3280069)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3280070)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (3280070)------------------------------
% 0.17/0.47 % (3280070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3280070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3280070)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3280070)Termination reason: Refutation
% 0.17/0.47 % (3280070)Time elapsed: 0.003 s
% 0.17/0.47 % (3280070)Peak memory usage: 11 MB
% 0.17/0.47 % (3280070)Instructions burned: 6 (million)
% 0.17/0.47 % (3280063)Success in time 0.033 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------