%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM014-1 : 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 : n014.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 04:52:43 PM UTC 2026
% Result : Unsatisfiable 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 13 unt; 3 nHn; 19 RR)
% Number of literals : 40 ( 0 equ; 19 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 34 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(remainder,axiom,
( divides(X1,X2)
| divides(X1,X3)
| ~ prime(X1)
| ~ product(X2,X3,X4)
| ~ divides(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',remainder) ).
cnf(commutativity,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity) ).
cnf(divides,axiom,
( divides(X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides) ).
cnf(square,axiom,
product(X1,X1,square(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square) ).
cnf(a_equals_b_squared_by_c_squared,hypothesis,
product(a,square(c),square(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_squared_by_c_squared) ).
cnf(prove_a_divides_b,negated_conjecture,
~ divides(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divides_b) ).
cnf(a_is_prime,hypothesis,
prime(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
cnf(i_0_7,axiom,
( divides(X1,X2)
| divides(X1,X3)
| ~ prime(X1)
| ~ product(X2,X3,X4)
| ~ divides(X1,X4) ),
remainder,
[final] ).
cnf(i_0_8,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity,
[final] ).
cnf(i_0_9,axiom,
( divides(X1,X3)
| ~ product(X1,X2,X3) ),
divides,
[final] ).
cnf(i_0_10,axiom,
product(X1,X1,square(X1)),
square,
[final] ).
cnf(i_0_11,hypothesis,
product(a,square(c),square(b)),
a_equals_b_squared_by_c_squared,
[final] ).
cnf(i_0_12,negated_conjecture,
~ divides(a,b),
prove_a_divides_b,
[final] ).
cnf(i_0_13,hypothesis,
prime(a),
a_is_prime,
[final] ).
cnf(i_0_14,plain,
product(square(c),a,square(b)),
inference(scs_inference,[],[i_0_11,i_0_8]) ).
cnf(i_0_15,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_16,plain,
~ product(a,X1,b),
inference(scs_inference,[],[i_0_12,i_0_11,i_0_8,i_0_9]) ).
cnf(i_0_17,plain,
( divides(X1,X2)
| ~ product(X1,X3,X2) ),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_18,plain,
~ divides(a,square(b)),
inference(scs_inference,[],[i_0_12,i_0_10,i_0_13,i_0_11,i_0_8,i_0_9,i_0_7]) ).
cnf(i_0_19,plain,
product(X1,X1,square(X1)),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_20,plain,
( ~ prime(X1)
| ~ divides(X1,X2)
| divides(X1,X3)
| ~ product(X3,X4,X2)
| divides(X1,X4) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_21,plain,
$false,
inference(scs_inference,[],[i_0_18,i_0_11,i_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM014-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n014.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 : Tue May 5 00:06:36 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.63 % Total time : 1.270s
%------------------------------------------------------------------------------