%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:31:49 AM UTC 2026
% Result : Unsatisfiable 8.13s 7.26s
% Output : CNFRefutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of clauses : 76 ( 76 unt; 0 nHn; 27 RR)
% Number of literals : 76 ( 75 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 123 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(X0,X0,X1,X2) = X1 ).
cnf(ifeq_axiom_001,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(less_equal_quotient,axiom,
ifeq(quotient(X0,X1,zero),true,'less$uequal'(X0,X1),true) = true ).
cnf(divisor_existence,axiom,
ifeq(quotient(X0,X1,X2),true,'less$uequal'(X2,X0),true) = true ).
cnf(quotient_property,axiom,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X3,X4,X5),true,ifeq(quotient(X6,X4,X1),true,ifeq(quotient(X7,X4,X0),true,ifeq(quotient(X7,X6,X3),true,'less$uequal'(X2,X5),true),true),true),true),true) = true ).
cnf(less_equal_and_equal,axiom,
ifeq2('less$uequal'(X0,X1),true,ifeq2('less$uequal'(X1,X0),true,X1,X0),X0) = X0 ).
cnf(identity_is_largest,axiom,
'less$uequal'(X0,identity) = true ).
cnf(closure,axiom,
quotient(X0,X1,divide(X0,X1)) = true ).
cnf(x_divide_x_is_zero,axiom,
quotient(X0,X0,zero) = true ).
cnf(x_divde_zero_is_x,axiom,
quotient(X0,zero,X0) = true ).
cnf(xQyLEz_implies_xQzLEy,axiom,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X4),true,ifeq('less$uequal'(X4,X1),true,'less$uequal'(X2,X3),true),true),true) = true ).
cnf(xLEy_implies_zQyLEzQx,axiom,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X4),true,ifeq('less$uequal'(X3,X1),true,'less$uequal'(X2,X4),true),true),true) = true ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa) = true ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,'idQ$uidQa') = true ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(idQa,'idQ$uidQa','idQa$uQ$u$uidQ$uidQa') = true ).
cnf(prove_idQa_equals_idQa_Q__idQ_idQa,negated_conjecture,
idQa != 'idQa$uQ$u$uidQ$uidQa' ).
cnf(c0,plain,
ifeq2(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom_001]) ).
cnf(c3,plain,
ifeq(quotient(X0,X1,zero),true,'less$uequal'(X0,X1),true) = true,
inference(clausification,[status(esa)],[less_equal_quotient]) ).
cnf(c4,plain,
ifeq(quotient(X0,X1,X2),true,'less$uequal'(X2,X0),true) = true,
inference(clausification,[status(esa)],[divisor_existence]) ).
cnf(c5,plain,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X3,X4,X5),true,ifeq(quotient(X6,X4,X1),true,ifeq(quotient(X7,X4,X0),true,ifeq(quotient(X7,X6,X3),true,'less$uequal'(X2,X5),true),true),true),true),true) = true,
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c7,plain,
ifeq2('less$uequal'(X0,X1),true,ifeq2('less$uequal'(X1,X0),true,X1,X0),X0) = X0,
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(c8,plain,
'less$uequal'(X0,identity) = true,
inference(clausification,[status(esa)],[identity_is_largest]) ).
cnf(c9,plain,
quotient(X0,X1,divide(X0,X1)) = true,
inference(clausification,[status(esa)],[closure]) ).
cnf(c13,plain,
quotient(X0,X0,zero) = true,
inference(clausification,[status(esa)],[x_divide_x_is_zero]) ).
cnf(c14,plain,
quotient(X0,zero,X0) = true,
inference(clausification,[status(esa)],[x_divde_zero_is_x]) ).
cnf(c16,plain,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X4),true,ifeq('less$uequal'(X4,X1),true,'less$uequal'(X2,X3),true),true),true) = true,
inference(clausification,[status(esa)],[xQyLEz_implies_xQzLEy]) ).
cnf(c17,plain,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X4),true,ifeq('less$uequal'(X3,X1),true,'less$uequal'(X2,X4),true),true),true) = true,
inference(clausification,[status(esa)],[xLEy_implies_zQyLEzQx]) ).
cnf(c19,plain,
quotient(identity,a,idQa) = true,
inference(clausification,[status(esa)],[identity_divide_a]) ).
cnf(c20,plain,
quotient(identity,idQa,'idQ$uidQa') = true,
inference(clausification,[status(esa)],[identity_divide_idQa]) ).
cnf(c21,plain,
quotient(idQa,'idQ$uidQa','idQa$uQ$u$uidQ$uidQa') = true,
inference(clausification,[status(esa)],[identity_divide_idQ_idQa]) ).
cnf(c22,plain,
idQa != 'idQa$uQ$u$uidQ$uidQa',
inference(clausification,[status(esa)],[prove_idQa_equals_idQa_Q__idQ_idQa]) ).
cnf(d0,plain,
ifeq(true,true,'less$uequal'(divide(X0,X1),X0),true) = true,
inference(superposition,[status(thm)],[c9,c4]) ).
cnf(d1,plain,
'less$uequal'(divide(X0,X1),X0) = true,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
ifeq2('less$uequal'(X0,divide(X0,X1)),true,ifeq2(true,true,divide(X0,X1),X0),X0) = X0,
inference(superposition,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
ifeq2('less$uequal'(X0,divide(X0,X1)),true,divide(X0,X1),X0) = X0,
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq(true,true,ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,zero),true,ifeq(quotient(X5,X2,X0),true,ifeq(quotient(X5,X4,X1),true,'less$uequal'(X0,X3),true),true),true),true),true) = true,
inference(superposition,[status(thm)],[c14,c5]) ).
cnf(d5,plain,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X3,X1,zero),true,ifeq(quotient(X4,X1,X5),true,ifeq(quotient(X4,X3,X0),true,'less$uequal'(X5,X2),true),true),true),true) = true,
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
ifeq(quotient(X0,a,X1),true,ifeq(quotient(X2,a,zero),true,ifeq(true,true,ifeq(quotient(identity,X2,X0),true,'less$uequal'(idQa,X1),true),true),true),true) = true,
inference(superposition,[status(thm)],[c19,d5]) ).
cnf(d7,plain,
ifeq(quotient(X1,a,X2),true,ifeq(quotient(X0,a,zero),true,ifeq(quotient(identity,X0,X1),true,'less$uequal'(idQa,X2),true),true),true) = true,
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
ifeq(quotient(idQa,a,X0),true,ifeq(quotient(a,a,zero),true,ifeq(true,true,'less$uequal'(idQa,X0),true),true),true) = true,
inference(superposition,[status(thm)],[c19,d7]) ).
cnf(d9,plain,
ifeq(quotient(idQa,a,X0),true,ifeq(true,true,ifeq(true,true,'less$uequal'(idQa,X0),true),true),true) = true,
inference(demodulation,[status(thm)],[d8,c13]) ).
cnf(d10,plain,
ifeq(quotient(idQa,a,X0),true,ifeq(true,true,'less$uequal'(idQa,X0),true),true) = true,
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
ifeq(quotient(idQa,a,X0),true,'less$uequal'(idQa,X0),true) = true,
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
ifeq(true,true,'less$uequal'(idQa,divide(idQa,a)),true) = true,
inference(superposition,[status(thm)],[c9,d11]) ).
cnf(d13,plain,
'less$uequal'(idQa,divide(idQa,a)) = true,
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
ifeq2(true,true,divide(idQa,a),idQa) = idQa,
inference(superposition,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
divide(idQa,a) = idQa,
inference(demodulation,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
ifeq(true,true,ifeq(quotient(X0,X2,X3),true,ifeq('less$uequal'(X2,X1),true,'less$uequal'(divide(X0,X1),X3),true),true),true) = true,
inference(superposition,[status(thm)],[c9,c17]) ).
cnf(d17,plain,
ifeq(quotient(X0,X1,X2),true,ifeq('less$uequal'(X1,X3),true,'less$uequal'(divide(X0,X3),X2),true),true) = true,
inference(demodulation,[status(thm)],[d16,c1]) ).
cnf(d18,plain,
ifeq(true,true,ifeq('less$uequal'('idQ$uidQa',X0),true,'less$uequal'(divide(idQa,X0),'idQa$uQ$u$uidQ$uidQa'),true),true) = true,
inference(superposition,[status(thm)],[c21,d17]) ).
cnf(d19,plain,
ifeq('less$uequal'('idQ$uidQa',X0),true,'less$uequal'(divide(idQa,X0),'idQa$uQ$u$uidQ$uidQa'),true) = true,
inference(demodulation,[status(thm)],[d18,c1]) ).
cnf(d20,plain,
ifeq(true,true,'less$uequal'(X0,X0),true) = true,
inference(superposition,[status(thm)],[c13,c3]) ).
cnf(d21,plain,
'less$uequal'(X0,X0) = true,
inference(demodulation,[status(thm)],[d20,c1]) ).
cnf(d22,plain,
ifeq(true,true,ifeq(quotient(identity,X0,X1),true,ifeq('less$uequal'(X1,idQa),true,'less$uequal'('idQ$uidQa',X0),true),true),true) = true,
inference(superposition,[status(thm)],[c20,c16]) ).
cnf(d23,plain,
ifeq(quotient(identity,X0,X1),true,ifeq('less$uequal'(X1,idQa),true,'less$uequal'('idQ$uidQa',X0),true),true) = true,
inference(demodulation,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
ifeq(true,true,ifeq('less$uequal'(idQa,idQa),true,'less$uequal'('idQ$uidQa',a),true),true) = true,
inference(superposition,[status(thm)],[c19,d23]) ).
cnf(d25,plain,
ifeq('less$uequal'(idQa,idQa),true,'less$uequal'('idQ$uidQa',a),true) = true,
inference(demodulation,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
ifeq(true,true,'less$uequal'('idQ$uidQa',a),true) = true,
inference(demodulation,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
'less$uequal'('idQ$uidQa',a) = true,
inference(demodulation,[status(thm)],[d26,c1]) ).
cnf(d28,plain,
ifeq(true,true,'less$uequal'(divide(idQa,a),'idQa$uQ$u$uidQ$uidQa'),true) = true,
inference(superposition,[status(thm)],[d27,d19]) ).
cnf(d29,plain,
'less$uequal'(divide(idQa,a),'idQa$uQ$u$uidQ$uidQa') = true,
inference(demodulation,[status(thm)],[d28,c1]) ).
cnf(d30,plain,
'less$uequal'(idQa,'idQa$uQ$u$uidQ$uidQa') = true,
inference(demodulation,[status(thm)],[d29,d15]) ).
cnf(d31,plain,
ifeq(true,true,'less$uequal'('idQa$uQ$u$uidQ$uidQa',idQa),true) = true,
inference(superposition,[status(thm)],[c21,c4]) ).
cnf(d32,plain,
'less$uequal'('idQa$uQ$u$uidQ$uidQa',idQa) = true,
inference(demodulation,[status(thm)],[d31,c1]) ).
cnf(d33,plain,
ifeq2('less$uequal'(idQa,'idQa$uQ$u$uidQ$uidQa'),true,ifeq2(true,true,'idQa$uQ$u$uidQ$uidQa',idQa),idQa) = idQa,
inference(superposition,[status(thm)],[d32,c7]) ).
cnf(d34,plain,
ifeq2('less$uequal'(idQa,'idQa$uQ$u$uidQ$uidQa'),true,'idQa$uQ$u$uidQ$uidQa',idQa) = idQa,
inference(demodulation,[status(thm)],[d33,c0]) ).
cnf(d35,plain,
ifeq2(true,true,'idQa$uQ$u$uidQ$uidQa',idQa) = idQa,
inference(demodulation,[status(thm)],[d34,d30]) ).
cnf(d36,plain,
'idQa$uQ$u$uidQ$uidQa' = idQa,
inference(demodulation,[status(thm)],[d35,c0]) ).
cnf(d37,plain,
idQa != idQa,
inference(demodulation,[status(thm)],[c22,d36]) ).
cnf(d38,plain,
ifeq2(true,true,ifeq2('less$uequal'(identity,X0),true,identity,X0),X0) = X0,
inference(superposition,[status(thm)],[c8,c7]) ).
cnf(d39,plain,
ifeq2('less$uequal'(identity,X0),true,identity,X0) = X0,
inference(demodulation,[status(thm)],[d38,c0]) ).
cnf(d40,plain,
ifeq2('less$uequal'(X0,identity),true,X0,X0) = X0,
inference(superposition,[status(thm)],[d39,c7]) ).
cnf(d41,plain,
ifeq2(true,true,X0,X0) = X0,
inference(demodulation,[status(thm)],[d40,c8]) ).
cnf(d42,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d41,c0]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,d37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:58:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.13/7.26 % SZS status Unsatisfiable for theBenchmark.p
% 8.13/7.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------