%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE022+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Thu Sep 24 08:46:53 AM UTC 2026
% Result : Theorem 268.35s 268.68s
% Output : Proof 270.82s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('KLE001+0.ax',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE001+0.ax',additive_associativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('KLE001+0.ax',additive_identity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('KLE001+0.ax',additive_idempotence) ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE001+0.ax',multiplicative_associativity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('KLE001+0.ax',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE001+0.ax',right_distributivity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE001+0.ax',left_distributivity) ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('KLE001+0.ax',left_annihilation) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('KLE001+0.ax',order) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('KLE001+1.ax',test_1) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('KLE001+1.ax',test_2) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('KLE001+1.ax',test_3) ).
fof(test_4,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('KLE001+1.ax',test_4) ).
fof(test_deMorgan1,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
file('KLE001+2.ax',test_deMorgan1) ).
fof(test_deMorgan2,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
file('KLE001+2.ax',test_deMorgan2) ).
fof(goals,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
& leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) ) ),
file('theBenchmark.p',goals) ).
fof(f_1_1,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(fof_nnf,[status(thm)],[additive_commutativity]) ).
fof(f_1_2,plain,
! [U_1,U_0] : addition(U_1,U_0) = addition(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] : addition(U_1,U_0) = addition(U_0,U_1),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
addition(U_1,U_0) = addition(U_0,U_1),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(fof_nnf,[status(thm)],[additive_associativity]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] : addition(U_2,addition(U_3,U_4)) = addition(addition(U_2,U_3),U_4),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_4,U_2] : addition(U_2,addition(U_3,U_4)) = addition(addition(U_2,U_3),U_4),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
addition(U_2,addition(U_3,U_4)) = addition(addition(U_2,U_3),U_4),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] : addition(A,zero) = A,
inference(fof_nnf,[status(thm)],[additive_identity]) ).
fof(f_3_2,plain,
! [U_5] : addition(U_5,zero) = U_5,
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_5] : addition(U_5,zero) = U_5,
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
addition(U_5,zero) = U_5,
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] : addition(A,A) = A,
inference(fof_nnf,[status(thm)],[additive_idempotence]) ).
fof(f_4_2,plain,
! [U_6] : addition(U_6,U_6) = U_6,
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_6] : addition(U_6,U_6) = U_6,
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
addition(U_6,U_6) = U_6,
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(fof_nnf,[status(thm)],[multiplicative_associativity]) ).
fof(f_5_2,plain,
! [U_9,U_8,U_7] : multiplication(U_9,multiplication(U_8,U_7)) = multiplication(multiplication(U_9,U_8),U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_7,U_8,U_9] : multiplication(U_9,multiplication(U_8,U_7)) = multiplication(multiplication(U_9,U_8),U_7),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
multiplication(U_9,multiplication(U_8,U_7)) = multiplication(multiplication(U_9,U_8),U_7),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] : multiplication(A,one) = A,
inference(fof_nnf,[status(thm)],[multiplicative_right_identity]) ).
fof(f_6_2,plain,
! [U_10] : multiplication(U_10,one) = U_10,
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_10] : multiplication(U_10,one) = U_10,
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
multiplication(U_10,one) = U_10,
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] : multiplication(one,A) = A,
inference(fof_nnf,[status(thm)],[multiplicative_left_identity]) ).
fof(f_7_2,plain,
! [U_11] : multiplication(one,U_11) = U_11,
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_11] : multiplication(one,U_11) = U_11,
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
multiplication(one,U_11) = U_11,
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(fof_nnf,[status(thm)],[right_distributivity]) ).
fof(f_8_2,plain,
! [U_14,U_13,U_12] : multiplication(U_14,addition(U_13,U_12)) = addition(multiplication(U_14,U_13),multiplication(U_14,U_12)),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_12,U_13,U_14] : multiplication(U_14,addition(U_13,U_12)) = addition(multiplication(U_14,U_13),multiplication(U_14,U_12)),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
multiplication(U_14,addition(U_13,U_12)) = addition(multiplication(U_14,U_13),multiplication(U_14,U_12)),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(fof_nnf,[status(thm)],[left_distributivity]) ).
fof(f_9_2,plain,
! [U_17,U_16,U_15] : multiplication(addition(U_17,U_16),U_15) = addition(multiplication(U_17,U_15),multiplication(U_16,U_15)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_15,U_16,U_17] : multiplication(addition(U_17,U_16),U_15) = addition(multiplication(U_17,U_15),multiplication(U_16,U_15)),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
multiplication(addition(U_17,U_16),U_15) = addition(multiplication(U_17,U_15),multiplication(U_16,U_15)),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] : multiplication(A,zero) = zero,
inference(fof_nnf,[status(thm)],[right_annihilation]) ).
fof(f_10_2,plain,
! [U_18] : multiplication(U_18,zero) = zero,
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_18] : multiplication(U_18,zero) = zero,
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
multiplication(U_18,zero) = zero,
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] : multiplication(zero,A) = zero,
inference(fof_nnf,[status(thm)],[left_annihilation]) ).
fof(f_11_2,plain,
! [U_19] : multiplication(zero,U_19) = zero,
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_19] : multiplication(zero,U_19) = zero,
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
multiplication(zero,U_19) = zero,
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A,B] :
( ( leq(A,B)
| addition(A,B) != B )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(fof_nnf,[status(thm)],[order]) ).
fof(f_12_2,plain,
! [U_21,U_20] :
( ( leq(U_21,U_20)
| addition(U_21,U_20) != U_20 )
& ( addition(U_21,U_20) = U_20
| ~ leq(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_25,U_23] :
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 )
& ! [U_24,U_22] :
( addition(U_24,U_22) = U_22
| ~ leq(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_25,U_23] :
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 )
& ! [U_24,U_22] :
( addition(U_24,U_22) = U_22
| ~ leq(U_24,U_22) ) ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
( addition(U_24,U_22) = U_22
| ~ leq(U_24,U_22) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(f_13_2,plain,
! [U_28] :
( ( test(U_28)
| ! [U_27] : ~ complement(U_27,U_28) )
& ( ? [U_26] : complement(U_26,U_28)
| ~ test(U_28) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_30] :
( test(U_30)
| ! [U_27] : ~ complement(U_27,U_30) )
& ! [U_29] :
( ? [U_26] : complement(U_26,U_29)
| ~ test(U_29) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_30] :
( test(U_30)
| ! [U_27] : ~ complement(U_27,U_30) )
& ! [U_29] :
( complement(sK1(U_29),U_29)
| ~ test(U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_26,sK1(U_29))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_27,U_30] :
( test(U_30)
| ~ complement(U_27,U_30) )
& ! [U_29] :
( complement(sK1(U_29),U_29)
| ~ test(U_29) ) ),
inference(definitional_conversion,[status(esa)],[f_13_4]) ).
cnf(f_13_6,plain,
( complement(sK1(U_29),U_29)
| ~ test(U_29) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_7,plain,
( test(U_30)
| ~ complement(U_27,U_30) ),
inference(clausify,[status(thm)],[f_13_5]) ).
fof(f_14_1,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(fof_nnf,[status(thm)],[test_2]) ).
fof(f_14_2,plain,
! [U_32,U_31] :
( ( complement(U_31,U_32)
| addition(U_32,U_31) != one
| multiplication(U_31,U_32) != zero
| multiplication(U_32,U_31) != zero )
& ( ( addition(U_32,U_31) = one
& multiplication(U_31,U_32) = zero
& multiplication(U_32,U_31) = zero )
| ~ complement(U_31,U_32) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_36,U_34] :
( complement(U_34,U_36)
| addition(U_36,U_34) != one
| multiplication(U_34,U_36) != zero
| multiplication(U_36,U_34) != zero )
& ! [U_35,U_33] :
( ( addition(U_35,U_33) = one
& multiplication(U_33,U_35) = zero
& multiplication(U_35,U_33) = zero )
| ~ complement(U_33,U_35) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_35,U_33] :
( addition(U_35,U_33) = one
| ~ sP0(U_35,U_33) )
& ! [U_35,U_33] :
( multiplication(U_33,U_35) = zero
| ~ sP0(U_35,U_33) )
& ! [U_35,U_33] :
( multiplication(U_35,U_33) = zero
| ~ sP0(U_35,U_33) )
& ! [U_34,U_36] :
( complement(U_34,U_36)
| addition(U_36,U_34) != one
| multiplication(U_34,U_36) != zero
| multiplication(U_36,U_34) != zero )
& ! [U_35,U_33] :
( sP0(U_35,U_33)
| ~ complement(U_33,U_35) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_14_3]) ).
cnf(f_14_5,plain,
( sP0(U_35,U_33)
| ~ complement(U_33,U_35) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( complement(U_34,U_36)
| addition(U_36,U_34) != one
| multiplication(U_34,U_36) != zero
| multiplication(U_36,U_34) != zero ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_7,plain,
( multiplication(U_35,U_33) = zero
| ~ sP0(U_35,U_33) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_8,plain,
( multiplication(U_33,U_35) = zero
| ~ sP0(U_35,U_33) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_9,plain,
( addition(U_35,U_33) = one
| ~ sP0(U_35,U_33) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(fof_nnf,[status(thm)],[test_3]) ).
fof(f_15_2,plain,
! [U_38,U_37] :
( ( ( c(U_38) = U_37
| ~ complement(U_38,U_37) )
& ( complement(U_38,U_37)
| c(U_38) != U_37 ) )
| ~ test(U_38) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_38] :
( ( ! [U_40] :
( c(U_38) = U_40
| ~ complement(U_38,U_40) )
& ! [U_39] :
( complement(U_38,U_39)
| c(U_38) != U_39 ) )
| ~ test(U_38) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_39,U_38,U_40] :
( c(U_38) = U_40
| ~ complement(U_38,U_40)
| ~ sP1(U_39,U_38,U_40) )
& ! [U_39,U_38,U_40] :
( complement(U_38,U_39)
| c(U_38) != U_39
| ~ sP1(U_39,U_38,U_40) )
& ! [U_39,U_38,U_40] :
( sP1(U_39,U_38,U_40)
| ~ test(U_38) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_15_3]) ).
cnf(f_15_5,plain,
( sP1(U_39,U_38,U_40)
| ~ test(U_38) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( complement(U_38,U_39)
| c(U_38) != U_39
| ~ sP1(U_39,U_38,U_40) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( c(U_38) = U_40
| ~ complement(U_38,U_40)
| ~ sP1(U_39,U_38,U_40) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(fof_nnf,[status(thm)],[test_4]) ).
fof(f_16_2,plain,
! [U_41] :
( c(U_41) = zero
| test(U_41) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_41] :
( c(U_41) = zero
| test(U_41) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( c(U_41) = zero
| test(U_41) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [X0,X1] :
( c(addition(X0,X1)) = multiplication(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(fof_nnf,[status(thm)],[test_deMorgan1]) ).
fof(f_17_2,plain,
! [U_43,U_42] :
( c(addition(U_43,U_42)) = multiplication(c(U_43),c(U_42))
| ~ test(U_42)
| ~ test(U_43) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_43,U_42] :
( c(addition(U_43,U_42)) = multiplication(c(U_43),c(U_42))
| ~ test(U_42)
| ~ test(U_43) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( c(addition(U_43,U_42)) = multiplication(c(U_43),c(U_42))
| ~ test(U_42)
| ~ test(U_43) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(fof_nnf,[status(thm)],[test_deMorgan2]) ).
fof(f_18_2,plain,
! [U_45,U_44] :
( c(multiplication(U_45,U_44)) = addition(c(U_45),c(U_44))
| ~ test(U_44)
| ~ test(U_45) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_44,U_45] :
( c(multiplication(U_45,U_44)) = addition(c(U_45),c(U_44))
| ~ test(U_44)
| ~ test(U_45) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( c(multiplication(U_45,U_44)) = addition(c(U_45),c(U_44))
| ~ test(U_44)
| ~ test(U_45) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
& leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) ) ),
inference(negate,[status(cth)],[goals]) ).
fof(f_19_2,negated_conjecture,
? [X0,X1] :
( ( ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
| ~ leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) )
& test(X1) ),
inference(fof_nnf,[status(thm)],[f_19_1]) ).
fof(f_19_3,negated_conjecture,
? [U_47,U_46] :
( ( ~ leq(addition(multiplication(U_47,U_46),multiplication(U_47,c(U_46))),U_47)
| ~ leq(U_47,addition(multiplication(U_47,U_46),multiplication(U_47,c(U_46)))) )
& test(U_46) ),
inference(variable_rename,[status(thm)],[f_19_2]) ).
fof(f_19_4,negated_conjecture,
? [U_46] :
( ( ~ leq(addition(multiplication(sK2,U_46),multiplication(sK2,c(U_46))),sK2)
| ~ leq(sK2,addition(multiplication(sK2,U_46),multiplication(sK2,c(U_46)))) )
& test(U_46) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_47,sK2)],[f_19_3]) ).
fof(f_19_5,negated_conjecture,
( ( ~ leq(addition(multiplication(sK2,sK3),multiplication(sK2,c(sK3))),sK2)
| ~ leq(sK2,addition(multiplication(sK2,sK3),multiplication(sK2,c(sK3)))) )
& test(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_46,sK3)],[f_19_4]) ).
fof(f_19_6,negated_conjecture,
( ( ~ leq(addition(multiplication(sK2,sK3),multiplication(sK2,c(sK3))),sK2)
| ~ leq(sK2,addition(multiplication(sK2,sK3),multiplication(sK2,c(sK3)))) )
& test(sK3) ),
inference(definitional_conversion,[status(esa)],[f_19_5]) ).
cnf(f_19_7,negated_conjecture,
test(sK3),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_8,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK3),multiplication(sK2,c(sK3))),sK2)
| ~ leq(sK2,addition(multiplication(sK2,sK3),multiplication(sK2,c(sK3)))) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( addition(Eq_x_0,Eq_x_1) = addition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( multiplication(Eq_x_0,Eq_x_1) = multiplication(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( c(Eq_x_0) = c(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( leq(Eq_y_0,Eq_y_1)
| ~ leq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( test(Eq_y_0)
| ~ test(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( complement(Eq_y_0,Eq_y_1)
| ~ complement(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE022+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 11:42:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 268.35/268.68 % SZS status Theorem for theBenchmark
% 268.35/268.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------