%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN005-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 04:28:30 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 20 unt; 0 nHn; 27 RR)
% Number of literals : 60 ( 4 equ; 30 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 3 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/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(yLEz,hypothesis,
less_equal(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',yLEz) ).
cnf(xLEy,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(prove_transitivity_of_less_equal,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
cnf(c_0_9,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_10,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_11,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_12,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_13,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X4,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X7,X5,X1)
| ~ quotient(X7,X6,X4) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,hypothesis,
less_equal(y,z),
yLEz ).
cnf(c_0_16,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,zero)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
quotient(y,z,zero),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_18,hypothesis,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,y,zero)
| ~ quotient(X2,z,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,hypothesis,
less_equal(x,y),
xLEy ).
cnf(c_0_20,hypothesis,
( less_equal(divide(divide(X1,z),zero),zero)
| ~ quotient(X1,y,zero) ),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_21,hypothesis,
quotient(x,y,zero),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_22,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_23,hypothesis,
less_equal(divide(divide(x,z),zero),zero),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,hypothesis,
divide(divide(x,z),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_12])]) ).
cnf(c_0_25,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_26,hypothesis,
quotient(divide(x,z),zero,zero),
inference(spm,[status(thm)],[c_0_10,c_0_24]) ).
cnf(c_0_27,hypothesis,
less_equal(divide(x,z),zero),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,hypothesis,
divide(x,z) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_12])]) ).
cnf(c_0_29,hypothesis,
quotient(x,z,zero),
inference(spm,[status(thm)],[c_0_10,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
~ less_equal(x,z),
prove_transitivity_of_less_equal ).
cnf(c_0_31,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN005-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n002.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 19:23:31 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------