%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG002-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n003.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 04:03:58 PM UTC 2026
% Result : Unsatisfiable 1.32s 1.74s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 13 unt; 8 nHn; 28 RR)
% Number of literals : 79 ( 0 equ; 37 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 55 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(square_to_0,axiom,
( product(X3,X3,additive_identity)
| ~ product(X1,X2,X3)
| ~ product(X1,X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_to_0) ).
cnf(product_and_inverse,axiom,
( greater_than_0(X1)
| product(X1,X1,additive_identity)
| greater_than_0(additive_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_inverse) ).
cnf(commutativity_of_product,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_product) ).
cnf(inverse_and_identity,axiom,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| product(X1,X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_and_identity) ).
cnf(not_abelian,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_abelian) ).
cnf(greater_than_0_square,axiom,
( ~ greater_than_0(X1)
| ~ product(X1,X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greater_than_0_square) ).
cnf(product_and_greater_than_0,axiom,
( greater_than_0(X3)
| ~ product(X1,X2,X3)
| ~ greater_than_0(X1)
| ~ greater_than_0(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_greater_than_0) ).
cnf(product_of_inverses1,axiom,
( product(additive_inverse(X1),additive_inverse(X2),X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_of_inverses1) ).
cnf(a_greater_than_0,hypothesis,
greater_than_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_greater_than_0) ).
cnf(prove_a_inverse_greater_than_0,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
cnf(product_to_inverse,axiom,
( product(X1,additive_inverse(X2),additive_inverse(X3))
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_inverse) ).
cnf(right_identity,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(c_0_12,axiom,
( product(X3,X3,additive_identity)
| ~ product(X1,X2,X3)
| ~ product(X1,X1,additive_identity) ),
square_to_0 ).
cnf(c_0_13,axiom,
( greater_than_0(X1)
| product(X1,X1,additive_identity)
| greater_than_0(additive_inverse(X1)) ),
product_and_inverse ).
cnf(c_0_14,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_product ).
cnf(c_0_15,axiom,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| product(X1,X1,additive_identity) ),
inverse_and_identity ).
cnf(c_0_16,plain,
( greater_than_0(additive_inverse(X1))
| greater_than_0(X1)
| product(X2,X2,additive_identity)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| product(X1,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
not_abelian ).
cnf(c_0_19,axiom,
( ~ greater_than_0(X1)
| ~ product(X1,X1,additive_identity) ),
greater_than_0_square ).
cnf(c_0_20,plain,
( greater_than_0(additive_inverse(multiplicative_inverse(X1)))
| greater_than_0(multiplicative_inverse(X1))
| product(X1,X1,additive_identity) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,axiom,
( greater_than_0(X3)
| ~ product(X1,X2,X3)
| ~ greater_than_0(X1)
| ~ greater_than_0(X2) ),
product_and_greater_than_0 ).
cnf(c_0_22,axiom,
( product(additive_inverse(X1),additive_inverse(X2),X3)
| ~ product(X1,X2,X3) ),
product_of_inverses1 ).
cnf(c_0_23,plain,
( greater_than_0(additive_inverse(multiplicative_inverse(X1)))
| greater_than_0(multiplicative_inverse(X1))
| ~ greater_than_0(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
greater_than_0(a),
a_greater_than_0 ).
cnf(c_0_25,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
prove_a_inverse_greater_than_0 ).
cnf(c_0_26,axiom,
( product(X1,additive_inverse(X2),additive_inverse(X3))
| ~ product(X1,X2,X3) ),
product_to_inverse ).
cnf(c_0_27,plain,
( greater_than_0(X1)
| ~ greater_than_0(additive_inverse(X2))
| ~ greater_than_0(additive_inverse(X3))
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,hypothesis,
greater_than_0(additive_inverse(multiplicative_inverse(a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,axiom,
product(X1,multiplicative_identity,X1),
right_identity ).
cnf(c_0_30,plain,
( greater_than_0(additive_inverse(X1))
| ~ greater_than_0(additive_inverse(X2))
| ~ greater_than_0(X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_31,hypothesis,
( greater_than_0(X1)
| ~ greater_than_0(additive_inverse(X2))
| ~ product(X2,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
product(multiplicative_identity,X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_29]) ).
cnf(c_0_33,hypothesis,
( greater_than_0(additive_inverse(X1))
| ~ greater_than_0(X2)
| ~ product(X2,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_34,hypothesis,
~ greater_than_0(additive_inverse(multiplicative_identity)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25]) ).
cnf(c_0_35,hypothesis,
product(a,a,additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_15]),c_0_24])]),c_0_34]) ).
cnf(c_0_36,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_35]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG002-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:13:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.32/1.74 % Version : CSE_E---1.7
% 1.32/1.74 % Problem : theBenchmark.p
% 1.32/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.32/1.74 % SZS output start CNFRefutation
% See solution above
% 1.32/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------