%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN009-1 : 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 : n007.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 04:28:33 PM UTC 2026
% Result : Unsatisfiable 9.33s 6.07s
% Output : CNFRefutation 9.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of clauses : 95 ( 47 unt; 0 nHn; 61 RR)
% Number of literals : 176 ( 29 equ; 83 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 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 : 183 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(prove_one_inversion_equals_three,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).
cnf(c_0_13,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_14,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_15,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_16,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_17,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,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_15,c_0_14]) ).
cnf(c_0_19,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,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_18,c_0_19]) ).
cnf(c_0_21,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X4,X4,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_22,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_23,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_24,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_25,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_26,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_28,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_29,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ quotient(X1,X2,zero) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_31,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_14,c_0_29]) ).
cnf(c_0_32,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28])]) ).
cnf(c_0_33,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_14,c_0_32]) ).
cnf(c_0_34,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_35,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,zero,X3)
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_36,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_37,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,divide(X2,zero),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_14]) ).
cnf(c_0_38,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_18,c_0_28]) ).
cnf(c_0_39,plain,
quotient(X1,identity,zero),
inference(spm,[status(thm)],[c_0_16,c_0_36]) ).
cnf(c_0_40,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_37,c_0_14]) ).
cnf(c_0_41,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(identity,X3,X2)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_43,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_40]),c_0_28])]) ).
cnf(c_0_44,plain,
( less_equal(divide(X1,X2),divide(X3,X4))
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X5,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_45,hypothesis,
( less_equal(divide(X1,idQ_idQa),zero)
| ~ quotient(X2,idQa,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_47,plain,
quotient(divide(X1,divide(X1,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_14,c_0_43]) ).
cnf(c_0_48,plain,
( less_equal(divide(X1,divide(X2,X3)),divide(X4,X3))
| ~ quotient(X5,X3,X1)
| ~ quotient(X5,X2,X4) ),
inference(spm,[status(thm)],[c_0_44,c_0_14]) ).
cnf(c_0_49,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
identity_divide_idQ_idQa ).
cnf(c_0_50,hypothesis,
less_equal(divide(divide(X1,idQa),idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_45,c_0_14]) ).
cnf(c_0_51,hypothesis,
( less_equal(divide(X1,idQa),zero)
| ~ quotient(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_46]) ).
cnf(c_0_52,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_47]),c_0_28])]) ).
cnf(c_0_53,hypothesis,
( less_equal(divide(idQ__idQ_idQa,divide(X1,idQ_idQa)),divide(X2,idQ_idQa))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,hypothesis,
divide(divide(X1,idQa),idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_50]),c_0_28])]) ).
cnf(c_0_55,hypothesis,
less_equal(divide(divide(X1,a),idQa),zero),
inference(spm,[status(thm)],[c_0_51,c_0_14]) ).
cnf(c_0_56,plain,
quotient(X1,divide(X1,zero),zero),
inference(spm,[status(thm)],[c_0_14,c_0_52]) ).
cnf(c_0_57,hypothesis,
( less_equal(divide(idQ__idQ_idQa,divide(X1,idQ_idQa)),zero)
| ~ quotient(identity,X1,divide(X2,idQa)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,hypothesis,
( less_equal(divide(X1,idQ__idQ_idQa),zero)
| ~ quotient(X2,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_49]) ).
cnf(c_0_59,hypothesis,
( less_equal(divide(idQ_idQa,divide(X1,idQa)),divide(X2,idQa))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_60,hypothesis,
divide(divide(X1,a),idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_55]),c_0_28])]) ).
cnf(c_0_61,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_56]),c_0_19])]) ).
cnf(c_0_62,hypothesis,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(spm,[status(thm)],[c_0_57,c_0_14]) ).
cnf(c_0_63,hypothesis,
less_equal(divide(divide(X1,idQ_idQa),idQ__idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_58,c_0_14]) ).
cnf(c_0_64,plain,
( less_equal(divide(X1,zero),divide(X2,X3))
| ~ quotient(X4,divide(X3,X5),X2)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_19]) ).
cnf(c_0_65,hypothesis,
( less_equal(divide(idQ_idQa,divide(X1,idQa)),zero)
| ~ quotient(identity,X1,divide(X2,a)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_67,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(divide(X3,X4),X5,X1)
| ~ quotient(X3,X5,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_68,plain,
quotient(X1,zero,X1),
inference(spm,[status(thm)],[c_0_14,c_0_61]) ).
cnf(c_0_69,hypothesis,
divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_62]),c_0_28])]) ).
cnf(c_0_70,hypothesis,
divide(divide(X1,idQ_idQa),idQ__idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_63]),c_0_28])]) ).
cnf(c_0_71,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,divide(X3,X5),X2)
| ~ quotient(X4,X3,X1) ),
inference(rw,[status(thm)],[c_0_64,c_0_61]) ).
cnf(c_0_72,hypothesis,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(spm,[status(thm)],[c_0_65,c_0_14]) ).
cnf(c_0_73,plain,
( X1 = zero
| ~ quotient(zero,X2,X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_28]) ).
cnf(c_0_74,plain,
( less_equal(divide(divide(X1,X2),X3),zero)
| ~ quotient(X1,zero,X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_75,hypothesis,
quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_14,c_0_69]) ).
cnf(c_0_76,hypothesis,
quotient(divide(X1,idQ_idQa),idQ__idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_14,c_0_70]) ).
cnf(c_0_77,plain,
( less_equal(X1,divide(divide(X2,divide(X3,X4)),X3))
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_14]) ).
cnf(c_0_78,hypothesis,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_72]),c_0_28])]) ).
cnf(c_0_79,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_73,c_0_14]) ).
cnf(c_0_80,plain,
( divide(divide(X1,X2),X3) = zero
| ~ quotient(X1,zero,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_74]),c_0_28])]) ).
cnf(c_0_81,hypothesis,
divide(idQa,idQ_idQa) = idQ__idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_75]),c_0_76])]) ).
cnf(c_0_82,hypothesis,
( less_equal(X1,zero)
| ~ quotient(idQ_idQa,a,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_83,hypothesis,
( divide(idQ__idQ_idQa,X1) = zero
| ~ quotient(idQa,zero,X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_84,hypothesis,
( less_equal(divide(idQa,divide(X1,a)),divide(X2,a))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
cnf(c_0_85,hypothesis,
( X1 = zero
| ~ quotient(idQ_idQa,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_82]),c_0_28])]) ).
cnf(c_0_86,plain,
( divide(X1,X2) = X1
| ~ quotient(X1,divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_87,hypothesis,
( quotient(idQ__idQ_idQa,X1,zero)
| ~ quotient(idQa,zero,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_83]) ).
cnf(c_0_88,hypothesis,
( divide(idQa,divide(X1,a)) = divide(X2,a)
| ~ quotient(divide(X2,a),divide(idQa,divide(X1,a)),zero)
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_84]) ).
cnf(c_0_89,hypothesis,
divide(idQ_idQa,a) = zero,
inference(spm,[status(thm)],[c_0_85,c_0_14]) ).
cnf(c_0_90,hypothesis,
quotient(divide(X1,a),idQa,zero),
inference(spm,[status(thm)],[c_0_14,c_0_60]) ).
cnf(c_0_91,hypothesis,
( divide(idQ__idQ_idQa,X1) = idQ__idQ_idQa
| ~ quotient(idQa,zero,divide(idQ__idQ_idQa,X1)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,hypothesis,
( divide(X1,a) = idQa
| ~ quotient(identity,idQ_idQa,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_61]),c_0_61]),c_0_90])]) ).
cnf(c_0_93,negated_conjecture,
idQa != idQ__idQ_idQa,
prove_one_inversion_equals_three ).
cnf(c_0_94,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_68]),c_0_49])]),c_0_93]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN009-1 : 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
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 19:09:09 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 9.33/6.07 % Version : CSE_E---1.7
% 9.33/6.07 % Problem : theBenchmark.p
% 9.33/6.07 % SZS status Unsatisfiable for theBenchmark.p
% 9.33/6.07 % SZS output start CNFRefutation
% See solution above
% 9.33/6.10 % Total time : 4.368s
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