%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP124-2.004 : 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 10:16:45 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 33
% Syntax : Number of formulae : 39 ( 31 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 61 ( 35 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f2,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).
fof(f3,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_then_e_4) ).
fof(f4,axiom,
greater(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_greater_e_1) ).
fof(f5,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_1) ).
fof(f6,axiom,
greater(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_1) ).
fof(f7,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_2) ).
fof(f8,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_2) ).
fof(f9,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_3) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ product(X0,e_1,X1)
| ~ next(X0,X2)
| ~ greater(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
fof(f11,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f12,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f13,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f14,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f15,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f16,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f17,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f18,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f19,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f20,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f21,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f22,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f23,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f24,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f25,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f26,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f27,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f28,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f30,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f31,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f32,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| equalish(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
fof(f33,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
fof(f34,plain,
~ group_element(e_1),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f35,plain,
~ group_element(e_2),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f36,plain,
~ group_element(e_3),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f37,plain,
~ group_element(e_4),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f38,plain,
! [X0,X1] :
( group_element(X0)
| group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4) ),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f82,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f34,f35,f36,f37,f15,f16,f17,f18,f19,f20,f21,f22,f23,f24,f25,f26,f38,f28,f29,f30,f31,f32,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:22:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42 Running first-order model finding
% 0.14/0.42 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
% 0.14/0.46 % (3279637)Will run a generic schedule for satisfiability detection.
% 0.14/0.46 % (3279660)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2681482178_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.46 % Detected minimum model sizes of [1]
% 0.14/0.46 % Detected maximum model sizes of [4]
% 0.14/0.46 % TRYING [1]
% 0.14/0.46 % TRYING [2]
% 0.14/0.46 % TRYING [3]
% 0.14/0.46 % TRYING [4]
% 0.14/0.46 % (3279660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3279637-3279660"...
% 0.14/0.46 % (3279660)...printing done.
% 0.14/0.46 % (3279660)Refutation found. Thanks to Tanya!
% 0.14/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.46 % (3279660)------------------------------
% 0.14/0.46 % (3279660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.46 % (3279660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.46 % (3279660)CaDiCaL version: 2.1.3
% 0.14/0.46 % (3279660)Termination reason: Refutation
% 0.14/0.46 % (3279660)Time elapsed: 0.004 s
% 0.14/0.46 % (3279660)Peak memory usage: 11 MB
% 0.14/0.46 % (3279660)Instructions burned: 13 (million)
% 0.14/0.46 % (3279637)Success in time 0.03 s
% 0.14/0.46 % Vampire exiting
%------------------------------------------------------------------------------