%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN010-2 : 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 : n001.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 04:28:34 PM UTC 2026
% Result : Unsatisfiable 6.16s 4.52s
% Output : CNFRefutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 39 ( 18 unt; 0 nHn; 33 RR)
% Number of literals : 84 ( 10 equ; 47 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 73 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(one_inversion_equals_three,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
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(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
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(x_divide_x_is_zero,axiom,
quotient(X1,X1,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(prove_idQa_equals_idQa_Q__idQ_idQa,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
cnf(c_0_13,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X3,X4) ),
one_inversion_equals_three ).
cnf(c_0_14,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_15,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_16,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
identity_divide_idQ_idQa ).
cnf(c_0_17,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_18,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_19,plain,
( X1 = divide(identity,X2)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X3,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_21,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
transitivity_of_less_equal ).
cnf(c_0_22,hypothesis,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,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_17,c_0_18]) ).
cnf(c_0_24,axiom,
quotient(X1,X1,zero),
x_divide_x_is_zero ).
cnf(c_0_25,hypothesis,
( divide(identity,idQ_idQa) = idQa
| ~ quotient(identity,X1,idQa) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_27,hypothesis,
( less_equal(X1,idQa)
| ~ less_equal(X1,idQa_Q__idQ_idQa) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_29,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,hypothesis,
divide(identity,idQ_idQa) = idQa,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_32,hypothesis,
( less_equal(X1,idQa)
| ~ quotient(X1,idQa_Q__idQ_idQa,zero) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,hypothesis,
( less_equal(X1,idQa_Q__idQ_idQa)
| ~ quotient(X2,idQ_idQa,idQa)
| ~ quotient(X2,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_34,hypothesis,
quotient(identity,idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_35,hypothesis,
( idQa = X1
| ~ quotient(X1,idQa_Q__idQ_idQa,zero)
| ~ less_equal(idQa,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
( less_equal(X1,idQa_Q__idQ_idQa)
| ~ quotient(identity,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
prove_idQa_equals_idQa_Q__idQ_idQa ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_24]),c_0_34])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN010-2 : 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
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 19:10:18 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 6.16/4.52 % Version : CSE_E---1.7
% 6.16/4.52 % Problem : theBenchmark.p
% 6.16/4.52 % SZS status Unsatisfiable for theBenchmark.p
% 6.16/4.52 % SZS output start CNFRefutation
% See solution above
% 6.16/4.54 % Total time : 3.369s
%------------------------------------------------------------------------------