%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD025-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:18:16 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 21 unt; 0 nHn; 35 RR)
% Number of literals : 57 ( 0 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(multiply_equals_v_10,negated_conjecture,
equalish(multiply(d,b),v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_equals_v_10) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(c_equals_d_8,negated_conjecture,
equalish(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_equals_d_8) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(a_equals_b_7,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_7) ).
cnf(multiply_equals_u_9,negated_conjecture,
equalish(multiply(a,c),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_equals_u_9) ).
cnf(v_not_equal_to_u_11,negated_conjecture,
~ equalish(v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_not_equal_to_u_11) ).
cnf(c_0_11,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_12,negated_conjecture,
equalish(multiply(d,b),v),
multiply_equals_v_10 ).
cnf(c_0_13,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_14,negated_conjecture,
equalish(c,d),
c_equals_d_8 ).
cnf(c_0_15,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,multiply(d,b)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( equalish(multiply(c,X1),multiply(d,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_18,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_19,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_20,negated_conjecture,
equalish(multiply(c,b),v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_21,plain,
( equalish(X1,multiply(X2,X3))
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(X1,multiply(X3,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
equalish(v,multiply(c,b)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_24,negated_conjecture,
equalish(v,multiply(b,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17]),c_0_23])]) ).
cnf(c_0_25,negated_conjecture,
equalish(multiply(b,c),v),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
equalish(a,b),
a_equals_b_7 ).
cnf(c_0_27,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,multiply(b,c)) ),
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( equalish(multiply(a,X1),multiply(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
equalish(multiply(a,c),u),
multiply_equals_u_9 ).
cnf(c_0_30,negated_conjecture,
equalish(multiply(a,c),v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23])]) ).
cnf(c_0_31,negated_conjecture,
( equalish(X1,u)
| ~ equalish(X1,multiply(a,c)) ),
inference(spm,[status(thm)],[c_0_11,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
equalish(v,multiply(a,c)),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ equalish(v,u),
v_not_equal_to_u_11 ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD025-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n009.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:27:26 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------