%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV489+3 : 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 : n017.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 09:03:48 AM UTC 2026
% Result : Theorem 234.22s 234.59s
% Output : Proof 236.65s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(int_leq,axiom,
! [I,J] :
( int_leq(I,J)
<=> ( I = J
| int_less(I,J) ) ),
file('theBenchmark.p',int_leq) ).
fof(int_less_transitive,axiom,
! [I,J,K] :
( ( int_less(J,K)
& int_less(I,J) )
=> int_less(I,K) ),
file('theBenchmark.p',int_less_transitive) ).
fof(int_less_irreflexive,axiom,
! [I,J] :
( int_less(I,J)
=> I != J ),
file('theBenchmark.p',int_less_irreflexive) ).
fof(int_less_total,axiom,
! [I,J] :
( int_leq(J,I)
| int_less(I,J) ),
file('theBenchmark.p',int_less_total) ).
fof(int_zero_one,axiom,
int_less(int_zero,int_one),
file('theBenchmark.p',int_zero_one) ).
fof(plus_commutative,axiom,
! [I,J] : plus(I,J) = plus(J,I),
file('theBenchmark.p',plus_commutative) ).
fof(plus_zero,axiom,
! [I] : plus(I,int_zero) = I,
file('theBenchmark.p',plus_zero) ).
fof(plus_and_order1,axiom,
! [I1,J1,I2,J2] :
( ( int_leq(I2,J2)
& int_less(I1,J1) )
=> int_leq(plus(I1,I2),plus(J1,J2)) ),
file('theBenchmark.p',plus_and_order1) ).
fof(plus_and_inverse,axiom,
! [I,J] :
( int_less(I,J)
<=> ? [K] :
( int_less(int_zero,K)
& plus(I,K) = J ) ),
file('theBenchmark.p',plus_and_inverse) ).
fof(one_successor_of_zero,axiom,
! [I] :
( int_less(int_zero,I)
<=> int_leq(int_one,I) ),
file('theBenchmark.p',one_successor_of_zero) ).
fof(real_constants,axiom,
real_zero != real_one,
file('theBenchmark.p',real_constants) ).
fof(qii,hypothesis,
! [I,J] :
( ( int_leq(J,n)
& int_leq(int_one,J)
& int_leq(I,n)
& int_leq(int_one,I) )
=> ( ! [C] :
( ( J = plus(I,C)
& int_less(int_zero,C) )
=> ! [K] :
( ( int_leq(K,I)
& int_leq(int_one,K) )
=> a(K,plus(K,C)) = real_zero ) )
& ! [K] :
( ( int_leq(K,J)
& int_leq(int_one,K) )
=> a(K,K) = real_one )
& ! [C] :
( ( I = plus(J,C)
& int_less(int_zero,C) )
=> ! [K] :
( ( int_leq(K,J)
& int_leq(int_one,K) )
=> a(plus(K,C),K) = real_zero ) ) ) ),
file('theBenchmark.p',qii) ).
fof(d,conjecture,
! [I,J] :
( ( I != J
& int_leq(J,n)
& int_leq(int_one,J)
& int_leq(I,n)
& int_leq(int_one,I) )
=> a(I,J) = real_zero ),
file('theBenchmark.p',d) ).
fof(f_1_1,plain,
! [I,J] :
( ( int_leq(I,J)
| ( I != J
& ~ int_less(I,J) ) )
& ( I = J
| int_less(I,J)
| ~ int_leq(I,J) ) ),
inference(fof_nnf,[status(thm)],[int_leq]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ( int_leq(U_1,U_0)
| ( U_1 != U_0
& ~ int_less(U_1,U_0) ) )
& ( U_1 = U_0
| int_less(U_1,U_0)
| ~ int_leq(U_1,U_0) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_5,U_3] :
( int_leq(U_5,U_3)
| ( U_5 != U_3
& ~ int_less(U_5,U_3) ) )
& ! [U_4,U_2] :
( U_4 = U_2
| int_less(U_4,U_2)
| ~ int_leq(U_4,U_2) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_3,U_5] :
( U_5 != U_3
| ~ sP0(U_3,U_5) )
& ! [U_3,U_5] :
( ~ int_less(U_5,U_3)
| ~ sP0(U_3,U_5) )
& ! [U_3,U_5] :
( int_leq(U_5,U_3)
| sP0(U_3,U_5) )
& ! [U_4,U_2] :
( U_4 = U_2
| int_less(U_4,U_2)
| ~ int_leq(U_4,U_2) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_1_3]) ).
cnf(f_1_5,plain,
( U_4 = U_2
| int_less(U_4,U_2)
| ~ int_leq(U_4,U_2) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( int_leq(U_5,U_3)
| sP0(U_3,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ int_less(U_5,U_3)
| ~ sP0(U_3,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_8,plain,
( U_5 != U_3
| ~ sP0(U_3,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [I,J,K] :
( int_less(I,K)
| ~ int_less(J,K)
| ~ int_less(I,J) ),
inference(fof_nnf,[status(thm)],[int_less_transitive]) ).
fof(f_2_2,plain,
! [U_8,U_7,U_6] :
( int_less(U_8,U_6)
| ~ int_less(U_7,U_6)
| ~ int_less(U_8,U_7) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_8,U_7,U_6] :
( int_less(U_8,U_6)
| ~ int_less(U_7,U_6)
| ~ int_less(U_8,U_7) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( int_less(U_8,U_6)
| ~ int_less(U_7,U_6)
| ~ int_less(U_8,U_7) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [I,J] :
( I != J
| ~ int_less(I,J) ),
inference(fof_nnf,[status(thm)],[int_less_irreflexive]) ).
fof(f_3_2,plain,
! [U_10,U_9] :
( U_10 != U_9
| ~ int_less(U_10,U_9) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_10,U_9] :
( U_10 != U_9
| ~ int_less(U_10,U_9) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( U_10 != U_9
| ~ int_less(U_10,U_9) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [I,J] :
( int_leq(J,I)
| int_less(I,J) ),
inference(fof_nnf,[status(thm)],[int_less_total]) ).
fof(f_4_2,plain,
! [U_12,U_11] :
( int_leq(U_11,U_12)
| int_less(U_12,U_11) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_11,U_12] :
( int_leq(U_11,U_12)
| int_less(U_12,U_11) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( int_leq(U_11,U_12)
| int_less(U_12,U_11) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
int_less(int_zero,int_one),
inference(fof_nnf,[status(thm)],[int_zero_one]) ).
fof(f_5_2,plain,
int_less(int_zero,int_one),
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
int_less(int_zero,int_one),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [I,J] : plus(I,J) = plus(J,I),
inference(fof_nnf,[status(thm)],[plus_commutative]) ).
fof(f_6_2,plain,
! [U_14,U_13] : plus(U_14,U_13) = plus(U_13,U_14),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_14,U_13] : plus(U_14,U_13) = plus(U_13,U_14),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
plus(U_14,U_13) = plus(U_13,U_14),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [I] : plus(I,int_zero) = I,
inference(fof_nnf,[status(thm)],[plus_zero]) ).
fof(f_7_2,plain,
! [U_15] : plus(U_15,int_zero) = U_15,
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_15] : plus(U_15,int_zero) = U_15,
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
plus(U_15,int_zero) = U_15,
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [I1,J1,I2,J2] :
( int_leq(plus(I1,I2),plus(J1,J2))
| ~ int_leq(I2,J2)
| ~ int_less(I1,J1) ),
inference(fof_nnf,[status(thm)],[plus_and_order1]) ).
fof(f_8_2,plain,
! [U_19,U_18,U_17,U_16] :
( int_leq(plus(U_19,U_17),plus(U_18,U_16))
| ~ int_leq(U_17,U_16)
| ~ int_less(U_19,U_18) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_16,U_18,U_19,U_17] :
( int_leq(plus(U_19,U_17),plus(U_18,U_16))
| ~ int_leq(U_17,U_16)
| ~ int_less(U_19,U_18) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( int_leq(plus(U_19,U_17),plus(U_18,U_16))
| ~ int_leq(U_17,U_16)
| ~ int_less(U_19,U_18) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [I,J] :
( ( int_less(I,J)
| ! [K] :
( ~ int_less(int_zero,K)
| plus(I,K) != J ) )
& ( ? [K] :
( int_less(int_zero,K)
& plus(I,K) = J )
| ~ int_less(I,J) ) ),
inference(fof_nnf,[status(thm)],[plus_and_inverse]) ).
fof(f_9_2,plain,
! [U_23,U_22] :
( ( int_less(U_23,U_22)
| ! [U_21] :
( ~ int_less(int_zero,U_21)
| plus(U_23,U_21) != U_22 ) )
& ( ? [U_20] :
( int_less(int_zero,U_20)
& plus(U_23,U_20) = U_22 )
| ~ int_less(U_23,U_22) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_27,U_25] :
( int_less(U_27,U_25)
| ! [U_21] :
( ~ int_less(int_zero,U_21)
| plus(U_27,U_21) != U_25 ) )
& ! [U_26,U_24] :
( ? [U_20] :
( int_less(int_zero,U_20)
& plus(U_26,U_20) = U_24 )
| ~ int_less(U_26,U_24) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_27,U_25] :
( int_less(U_27,U_25)
| ! [U_21] :
( ~ int_less(int_zero,U_21)
| plus(U_27,U_21) != U_25 ) )
& ! [U_26,U_24] :
( ( int_less(int_zero,sK1(U_26,U_24))
& plus(U_26,sK1(U_26,U_24)) = U_24 )
| ~ int_less(U_26,U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_20,sK1(U_26,U_24))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_26,U_24] :
( int_less(int_zero,sK1(U_26,U_24))
| ~ sP1(U_26,U_24) )
& ! [U_26,U_24] :
( plus(U_26,sK1(U_26,U_24)) = U_24
| ~ sP1(U_26,U_24) )
& ! [U_25,U_21,U_27] :
( int_less(U_27,U_25)
| ~ int_less(int_zero,U_21)
| plus(U_27,U_21) != U_25 )
& ! [U_26,U_24] :
( sP1(U_26,U_24)
| ~ int_less(U_26,U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_9_4]) ).
cnf(f_9_6,plain,
( sP1(U_26,U_24)
| ~ int_less(U_26,U_24) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( int_less(U_27,U_25)
| ~ int_less(int_zero,U_21)
| plus(U_27,U_21) != U_25 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( plus(U_26,sK1(U_26,U_24)) = U_24
| ~ sP1(U_26,U_24) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( int_less(int_zero,sK1(U_26,U_24))
| ~ sP1(U_26,U_24) ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_1,plain,
! [I] :
( ( int_less(int_zero,I)
| ~ int_leq(int_one,I) )
& ( int_leq(int_one,I)
| ~ int_less(int_zero,I) ) ),
inference(fof_nnf,[status(thm)],[one_successor_of_zero]) ).
fof(f_10_2,plain,
! [U_28] :
( ( int_less(int_zero,U_28)
| ~ int_leq(int_one,U_28) )
& ( int_leq(int_one,U_28)
| ~ int_less(int_zero,U_28) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_30] :
( int_less(int_zero,U_30)
| ~ int_leq(int_one,U_30) )
& ! [U_29] :
( int_leq(int_one,U_29)
| ~ int_less(int_zero,U_29) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_30] :
( int_less(int_zero,U_30)
| ~ int_leq(int_one,U_30) )
& ! [U_29] :
( int_leq(int_one,U_29)
| ~ int_less(int_zero,U_29) ) ),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
( int_leq(int_one,U_29)
| ~ int_less(int_zero,U_29) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( int_less(int_zero,U_30)
| ~ int_leq(int_one,U_30) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
real_zero != real_one,
inference(fof_nnf,[status(thm)],[real_constants]) ).
fof(f_11_2,plain,
real_zero != real_one,
inference(definitional_conversion,[status(esa)],[f_11_1]) ).
cnf(f_11_3,plain,
real_zero != real_one,
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [I,J] :
( ( ! [C] :
( ! [K] :
( a(K,plus(K,C)) = real_zero
| ~ int_leq(K,I)
| ~ int_leq(int_one,K) )
| J != plus(I,C)
| ~ int_less(int_zero,C) )
& ! [K] :
( a(K,K) = real_one
| ~ int_leq(K,J)
| ~ int_leq(int_one,K) )
& ! [C] :
( ! [K] :
( a(plus(K,C),K) = real_zero
| ~ int_leq(K,J)
| ~ int_leq(int_one,K) )
| I != plus(J,C)
| ~ int_less(int_zero,C) ) )
| ~ int_leq(J,n)
| ~ int_leq(int_one,J)
| ~ int_leq(I,n)
| ~ int_leq(int_one,I) ),
inference(fof_nnf,[status(thm)],[qii]) ).
fof(f_12_2,plain,
! [U_37,U_36] :
( ( ! [U_35] :
( ! [U_34] :
( a(U_34,plus(U_34,U_35)) = real_zero
| ~ int_leq(U_34,U_37)
| ~ int_leq(int_one,U_34) )
| U_36 != plus(U_37,U_35)
| ~ int_less(int_zero,U_35) )
& ! [U_33] :
( a(U_33,U_33) = real_one
| ~ int_leq(U_33,U_36)
| ~ int_leq(int_one,U_33) )
& ! [U_32] :
( ! [U_31] :
( a(plus(U_31,U_32),U_31) = real_zero
| ~ int_leq(U_31,U_36)
| ~ int_leq(int_one,U_31) )
| U_37 != plus(U_36,U_32)
| ~ int_less(int_zero,U_32) ) )
| ~ int_leq(U_36,n)
| ~ int_leq(int_one,U_36)
| ~ int_leq(U_37,n)
| ~ int_leq(int_one,U_37) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_31,U_32,U_33,U_34,U_35,U_36,U_37] :
( a(U_34,plus(U_34,U_35)) = real_zero
| ~ int_leq(U_34,U_37)
| ~ int_leq(int_one,U_34)
| U_36 != plus(U_37,U_35)
| ~ int_less(int_zero,U_35)
| ~ sP2(U_31,U_32,U_33,U_34,U_35,U_36,U_37) )
& ! [U_31,U_32,U_33,U_34,U_35,U_36,U_37] :
( a(U_33,U_33) = real_one
| ~ int_leq(U_33,U_36)
| ~ int_leq(int_one,U_33)
| ~ sP2(U_31,U_32,U_33,U_34,U_35,U_36,U_37) )
& ! [U_31,U_32,U_33,U_34,U_35,U_36,U_37] :
( a(plus(U_31,U_32),U_31) = real_zero
| ~ int_leq(U_31,U_36)
| ~ int_leq(int_one,U_31)
| U_37 != plus(U_36,U_32)
| ~ int_less(int_zero,U_32)
| ~ sP2(U_31,U_32,U_33,U_34,U_35,U_36,U_37) )
& ! [U_31,U_32,U_33,U_34,U_35,U_36,U_37] :
( sP2(U_31,U_32,U_33,U_34,U_35,U_36,U_37)
| ~ int_leq(U_36,n)
| ~ int_leq(int_one,U_36)
| ~ int_leq(U_37,n)
| ~ int_leq(int_one,U_37) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP2(U_31,U_32,U_33,U_34,U_35,U_36,U_37)
| ~ int_leq(U_36,n)
| ~ int_leq(int_one,U_36)
| ~ int_leq(U_37,n)
| ~ int_leq(int_one,U_37) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( a(plus(U_31,U_32),U_31) = real_zero
| ~ int_leq(U_31,U_36)
| ~ int_leq(int_one,U_31)
| U_37 != plus(U_36,U_32)
| ~ int_less(int_zero,U_32)
| ~ sP2(U_31,U_32,U_33,U_34,U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( a(U_33,U_33) = real_one
| ~ int_leq(U_33,U_36)
| ~ int_leq(int_one,U_33)
| ~ sP2(U_31,U_32,U_33,U_34,U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_7,plain,
( a(U_34,plus(U_34,U_35)) = real_zero
| ~ int_leq(U_34,U_37)
| ~ int_leq(int_one,U_34)
| U_36 != plus(U_37,U_35)
| ~ int_less(int_zero,U_35)
| ~ sP2(U_31,U_32,U_33,U_34,U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,negated_conjecture,
~ ! [I,J] :
( ( I != J
& int_leq(J,n)
& int_leq(int_one,J)
& int_leq(I,n)
& int_leq(int_one,I) )
=> a(I,J) = real_zero ),
inference(negate,[status(cth)],[d]) ).
fof(f_13_2,negated_conjecture,
? [I,J] :
( a(I,J) != real_zero
& I != J
& int_leq(J,n)
& int_leq(int_one,J)
& int_leq(I,n)
& int_leq(int_one,I) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_39,U_38] :
( a(U_39,U_38) != real_zero
& U_39 != U_38
& int_leq(U_38,n)
& int_leq(int_one,U_38)
& int_leq(U_39,n)
& int_leq(int_one,U_39) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_38] :
( a(sK2,U_38) != real_zero
& sK2 != U_38
& int_leq(U_38,n)
& int_leq(int_one,U_38)
& int_leq(sK2,n)
& int_leq(int_one,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_39,sK2)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
( a(sK2,sK3) != real_zero
& sK2 != sK3
& int_leq(sK3,n)
& int_leq(int_one,sK3)
& int_leq(sK2,n)
& int_leq(int_one,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_38,sK3)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( a(sK2,sK3) != real_zero
& sK2 != sK3
& int_leq(sK3,n)
& int_leq(int_one,sK3)
& int_leq(sK2,n)
& int_leq(int_one,sK2) ),
inference(definitional_conversion,[status(esa)],[f_13_5]) ).
cnf(f_13_7,negated_conjecture,
int_leq(int_one,sK2),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
int_leq(sK2,n),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,negated_conjecture,
int_leq(int_one,sK3),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_10,negated_conjecture,
int_leq(sK3,n),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_11,negated_conjecture,
sK2 != sK3,
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_12,negated_conjecture,
a(sK2,sK3) != real_zero,
inference(clausify,[status(thm)],[f_13_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,
( plus(Eq_x_0,Eq_x_1) = plus(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,
( a(Eq_x_0,Eq_x_1) = a(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,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( int_leq(Eq_y_0,Eq_y_1)
| ~ int_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_8,axiom,
( int_less(Eq_y_0,Eq_y_1)
| ~ int_less(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,
( 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_10,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(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,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| 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 : SWV489+3 : 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
% 0.08/0.39 % Computer : n017.cluster.edu
% 0.08/0.39 % Model : x86_64 x86_64
% 0.08/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.39 % Memory : 8046.5625MB
% 0.08/0.39 % OS : Linux 6.8.0-71-generic
% 0.08/0.39 % CPULimit : 300
% 0.08/0.39 % WCLimit : 300
% 0.08/0.39 % DateTime : Sun Sep 20 03:42:40 UTC 2026
% 0.08/0.39 % CPUTime :
% 234.22/234.59 % SZS status Theorem for theBenchmark
% 234.22/234.59 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------