%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN003-2 : TPTP v9.2.1. Released v1.0.0.
% 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 : n012.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 04:28:29 PM UTC 2026
% Result : Unsatisfiable 1.15s 1.66s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of clauses : 40 ( 23 unt; 0 nHn; 19 RR)
% Number of literals : 76 ( 6 equ; 38 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 103 ( 24 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(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
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(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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
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_x_divide_x_is_zero,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
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,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_12,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_13,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_14,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_15,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
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_12,c_0_13]) ).
cnf(c_0_17,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(divide(X3,X4),X5,X1)
| ~ quotient(X3,X5,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
( less_equal(divide(divide(divide(X1,X2),X3),X4),zero)
| ~ quotient(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_20,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_21,plain,
less_equal(divide(divide(divide(divide(X1,X2),X3),X1),zero),zero),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_22,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_23,plain,
divide(divide(divide(divide(X1,X2),X3),X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_24,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_25,plain,
quotient(divide(divide(divide(X1,X2),X3),X1),zero,zero),
inference(spm,[status(thm)],[c_0_10,c_0_23]) ).
cnf(c_0_26,plain,
less_equal(divide(divide(divide(X1,X2),X3),X1),zero),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,divide(X5,X6))
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_28,plain,
divide(divide(divide(X1,X2),X3),X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_22])]) ).
cnf(c_0_29,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X4,X4,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_10]) ).
cnf(c_0_30,plain,
quotient(divide(divide(X1,X2),X3),X1,zero),
inference(spm,[status(thm)],[c_0_10,c_0_28]) ).
cnf(c_0_31,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_31,c_0_10]) ).
cnf(c_0_33,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_32]),c_0_22])]) ).
cnf(c_0_34,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_10,c_0_33]) ).
cnf(c_0_35,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_36,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_35]),c_0_22])]) ).
cnf(c_0_37,negated_conjecture,
~ quotient(x,x,zero),
prove_x_divide_x_is_zero ).
cnf(c_0_38,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_10,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : HEN003-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.07 % 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
% 0.09/0.27 % Computer : n012.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Mon May 4 19:08:31 EDT 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.28 % start to proof: theBenchmark
% 1.15/1.66 % Version : CSE_E---1.7
% 1.15/1.66 % Problem : theBenchmark.p
% 1.15/1.66 % SZS status Unsatisfiable for theBenchmark.p
% 1.15/1.66 % SZS output start CNFRefutation
% See solution above
% 1.15/1.66 % Total time : 1.366s
%------------------------------------------------------------------------------