%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 10:16:43 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 60 ( 36 unt; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 167 ( 89 ~; 78 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_0,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_0_then_e_1) ).
fof(f2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
fof(f4,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_greater_e_0) ).
fof(f5,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_0) ).
fof(f6,axiom,
greater(e_3,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_0) ).
fof(f7,axiom,
greater(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).
fof(f8,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
fof(f9,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ cycle(X0,X2)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle1) ).
fof(f11,axiom,
! [X0] :
( ~ group_element(X0)
| cycle(X0,e_0)
| cycle(X0,e_1)
| cycle(X0,e_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle2) ).
fof(f12,axiom,
cycle(e_3,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle3) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X4] :
( ~ cycle(X0,X1)
| ~ cycle(X2,X3)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ next(X3,X4)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle4) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X4] :
( ~ cycle(X0,X1)
| ~ cycle(X2,e_0)
| ~ cycle(X3,X4)
| ~ next(X2,X3)
| ~ greater(X2,X0)
| ~ greater(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle5) ).
fof(f15,axiom,
! [X0,X1] :
( ~ cycle(X0,e_0)
| ~ product(X0,e_1,X1)
| ~ greater(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle6) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ cycle(X0,X1)
| ~ product(X0,e_1,X2)
| ~ greater(X1,e_0)
| ~ next(X0,X3)
| equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle7) ).
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f21,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f22,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f23,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f24,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f25,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f26,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f27,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f28,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f30,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f31,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_1) ).
fof(f32,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
fof(f33,plain,
~ greater(e_1,e_0),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f34,plain,
~ greater(e_2,e_0),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f35,plain,
~ greater(e_3,e_0),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f36,plain,
~ greater(e_2,e_1),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f37,plain,
~ greater(e_3,e_1),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f38,plain,
~ greater(e_3,e_2),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ cycle(X0,X2)
| ~ equalish(X1,X2) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f40,plain,
! [X0] :
( group_element(X0)
| cycle(X0,e_0)
| cycle(X0,e_1)
| cycle(X0,e_2) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f41,plain,
! [X2,X3,X0,X1,X4] :
( ~ cycle(X0,X1)
| ~ cycle(X2,X3)
| ~ next(X0,X2)
| greater(X1,e_0)
| ~ next(X3,X4)
| ~ equalish(X1,X4) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f42,plain,
! [X2,X3,X0,X1,X4] :
( ~ cycle(X0,X1)
| ~ cycle(X2,e_0)
| ~ cycle(X3,X4)
| ~ next(X2,X3)
| greater(X2,X0)
| greater(X1,X4) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f43,plain,
! [X0,X1] :
( ~ cycle(X0,e_0)
| ~ product(X0,e_1,X1)
| greater(X1,X0) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( ~ cycle(X0,X1)
| ~ product(X0,e_1,X2)
| greater(X1,e_0)
| ~ next(X0,X3)
| ~ equalish(X2,X3) ),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f45,plain,
~ group_element(e_1),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f46,plain,
~ group_element(e_2),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f47,plain,
~ group_element(e_3),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f48,plain,
equalish(e_1,e_2),
inference(consistent_polarity_flipping,[],[f20]) ).
fof(f49,plain,
equalish(e_1,e_3),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f50,plain,
equalish(e_2,e_1),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f51,plain,
equalish(e_2,e_3),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f52,plain,
equalish(e_3,e_1),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f53,plain,
equalish(e_3,e_2),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f54,plain,
! [X0,X1] :
( group_element(X0)
| group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3) ),
inference(consistent_polarity_flipping,[],[f26]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| ~ equalish(X2,X3) ),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| ~ equalish(X1,X3) ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| ~ equalish(X0,X3) ),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| ~ equalish(X0,X3) ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f59,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| ~ equalish(X1,X4) ),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f121,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f1,f2,f3,f33,f34,f35,f36,f37,f38,f39,f40,f12,f41,f42,f43,f44,f45,f46,f47,f48,f49,f50,f51,f52,f53,f54,f55,f56,f57,f30,f58,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:22:09 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.46 % (2068577)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (2068582)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1577048526_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.46 % Detected minimum model sizes of [1]
% 0.13/0.46 % Detected maximum model sizes of [4]
% 0.13/0.46 % TRYING [1]
% 0.13/0.46 % TRYING [2]
% 0.13/0.46 % TRYING [3]
% 0.13/0.46 % TRYING [4]
% 0.13/0.46 % (2068583)% WARNING: option uhcvi not known.
% 0.13/0.46 % (2068582) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2068577-2068582"...
% 0.13/0.46 % (2068582)...printing done.
% 0.13/0.46 % (2068582)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46 % (2068582)------------------------------
% 0.19/0.46 % (2068582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.46 % (2068582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.46 % (2068582)CaDiCaL version: 2.1.3
% 0.19/0.46 % (2068582)Termination reason: Refutation
% 0.19/0.46 % (2068582)Time elapsed: 0.005 s
% 0.19/0.46 % (2068582)Peak memory usage: 12 MB
% 0.19/0.46 % (2068582)Instructions burned: 19 (million)
% 0.19/0.46 % (2068577)Success in time 0.033 s
% 0.19/0.46 % Vampire exiting
%------------------------------------------------------------------------------