%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN007-6 : 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 : n019.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 04:28:32 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.91s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 15 unt; 0 nHn; 24 RR)
% Number of literals : 59 ( 0 equ; 32 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 58 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_property,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(xLEy,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(transitivity_of_less_equal,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
cnf(zQy,hypothesis,
quotient(z,y,zQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQy) ).
cnf(prove_zQyLEzQx,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
cnf(zQx,hypothesis,
quotient(z,x,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQx) ).
cnf(c_0_10,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
quotient_property ).
cnf(c_0_11,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_12,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_13,hypothesis,
less_equal(x,y),
xLEy ).
cnf(c_0_14,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,zero)
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X3,X5) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,hypothesis,
quotient(x,y,zero),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_17,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_18,hypothesis,
( less_equal(X1,X2)
| ~ quotient(X3,y,X2)
| ~ quotient(X4,y,X1)
| ~ quotient(X4,x,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
transitivity_of_less_equal ).
cnf(c_0_20,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,hypothesis,
( less_equal(X1,divide(X2,y))
| ~ quotient(X3,y,X1)
| ~ quotient(X3,x,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,hypothesis,
quotient(z,y,zQy),
zQy ).
cnf(c_0_23,plain,
( less_equal(X1,X2)
| ~ less_equal(X1,divide(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
( less_equal(zQy,divide(X1,y))
| ~ quotient(z,x,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ less_equal(zQy,zQx),
prove_zQyLEzQx ).
cnf(c_0_26,hypothesis,
( less_equal(zQy,X1)
| ~ quotient(z,x,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,hypothesis,
quotient(z,x,zQx),
zQx ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.22 % Problem : HEN007-6 : TPTP v9.2.1. Released v1.0.0.
% 0.04/0.22 % 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
% 0.12/0.44 % Computer : n019.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8042.1875MB
% 0.12/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Mon May 4 19:08:59 EDT 2026
% 0.14/0.45 % CPUTime :
% 0.14/0.46 % start to proof: theBenchmark
% 1.33/1.91 % Version : CSE_E---1.7
% 1.33/1.91 % Problem : theBenchmark.p
% 1.33/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.91 % SZS output start CNFRefutation
% See solution above
% 1.33/1.91 % Total time : 1.376s
%------------------------------------------------------------------------------