%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : FLD039-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 09:49:40 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 53 ( 10 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 181 ( 84 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 141 ( 141 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X0)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X1,X2)
| ~ product(X3,X4,X0)
| ~ product(X4,X1,X5)
| ~ product(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
fof(f9,axiom,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( product(X0,X1,X2)
| ~ product(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X5)
| ~ product(X5,X6,X2)
| ~ product(X3,X6,X0)
| ~ product(X4,X6,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X1,X2)
| ~ sum(X3,X4,X0)
| ~ product(X3,X1,X5)
| ~ product(X4,X1,X6)
| ~ sum(X5,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
fof(f13,axiom,
! [X0,X1] :
( defined(add(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_addition) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
fof(f16,axiom,
! [X0,X1] :
( defined(multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
fof(f18,axiom,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f19,axiom,
! [X0,X1] :
( sum(X0,X1,add(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
fof(f20,axiom,
! [X0,X1] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
fof(f21,axiom,
! [X0,X1] :
( sum(additive_identity,X0,X1)
| ~ less_or_equal(X0,X1)
| ~ less_or_equal(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
fof(f22,axiom,
! [X2,X0,X1] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X0,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
fof(f23,axiom,
! [X0,X1] :
( less_or_equal(X0,X1)
| less_or_equal(X1,X0)
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X4] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X2,X3)
| ~ sum(X2,X4,X0)
| ~ sum(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
fof(f25,axiom,
! [X2,X0,X1] :
( less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2)
| ~ product(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_multiplication) ).
fof(f26,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',different_identities) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_1) ).
fof(f29,negated_conjecture,
sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
fof(f30,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X1,X2)
| sum(X0,X3,X4)
| sum(X3,X5,X1)
| sum(X4,X5,X2) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f31,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X1,X2)
| sum(X3,X4,X0)
| sum(X4,X1,X5)
| sum(X3,X5,X2) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ~ sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ~ sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| product(X0,X3,X4)
| product(X3,X5,X1)
| product(X4,X5,X2) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f36,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| product(X3,X4,X0)
| product(X4,X1,X5)
| product(X3,X5,X2) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f37,plain,
! [X0] :
( ~ product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f38,plain,
! [X0] :
( ~ product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f40,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X0,X1,X2)
| sum(X3,X4,X5)
| product(X5,X6,X2)
| product(X3,X6,X0)
| product(X4,X6,X1) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f41,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X1,X2)
| sum(X3,X4,X0)
| product(X3,X1,X5)
| product(X4,X1,X6)
| sum(X5,X6,X2) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f42,plain,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| ~ sum(additive_identity,X0,additive_identity) ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f43,plain,
! [X0,X1] :
( ~ sum(X0,X1,add(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f44,plain,
! [X0,X1] :
( ~ product(X0,X1,multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
inference(consistent_polarity_flipping,[],[f20]) ).
fof(f45,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| less_or_equal(X0,X1)
| less_or_equal(X1,X0) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ less_or_equal(X0,X1)
| less_or_equal(X0,X2)
| less_or_equal(X2,X1) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f47,plain,
! [X0,X1] :
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(X1,X0)
| ~ defined(X0)
| ~ defined(X1) ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f48,plain,
! [X2,X3,X0,X1,X4] :
( ~ less_or_equal(X0,X1)
| less_or_equal(X2,X3)
| sum(X2,X4,X0)
| sum(X3,X4,X1) ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_identity,X1)
| less_or_equal(additive_identity,X2)
| product(X1,X2,X0) ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f50,plain,
sum(additive_identity,additive_identity,multiplicative_identity),
inference(consistent_polarity_flipping,[],[f26]) ).
fof(f51,plain,
sum(additive_identity,a,additive_identity),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f52,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f101,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f30,f31,f32,f33,f34,f35,f36,f37,f38,f39,f40,f41,f13,f14,f15,f16,f17,f42,f43,f44,f45,f46,f47,f48,f49,f50,f27,f51,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD039-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 % Computer : n006.cluster.edu
% 0.07/0.22 % Model : x86_64 x86_64
% 0.07/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.22 % Memory : 8046.5625MB
% 0.07/0.22 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Tue Sep 29 00:33:40 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.26 Running first-order model finding
% 0.07/0.26 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
% 0.19/0.30 % (361831)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (361836)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3987630913_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % TRYING [1]
% 0.19/0.30 % TRYING [2]
% 0.19/0.30 % (361836) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-361831-361836"...
% 0.19/0.30 % (361836)...printing done.
% 0.19/0.30 % (361836)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.30 % (361836)------------------------------
% 0.19/0.30 % (361836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (361836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (361836)CaDiCaL version: 2.1.3
% 0.19/0.30 % (361836)Termination reason: Refutation
% 0.19/0.30 % (361836)Time elapsed: 0.002 s
% 0.19/0.30 % (361836)Peak memory usage: 11 MB
% 0.19/0.30 % (361836)Instructions burned: 6 (million)
% 0.19/0.30 % (361831)Success in time 0.035 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------