%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE005+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : Sat Jun 21 05:12:49 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 48
% Syntax : Number of formulae : 123 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 603 ( 315 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 839 ( 387 ~; 266 |; 36 &)
% ( 144 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 183 ( 161 !; 4 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
tff(complement_type,type,
complement: ( $i * $i ) > $o ).
tff(zero_type,type,
zero: $i ).
tff(one_type,type,
one: $i ).
tff(tptp_fun_X1_0_type,type,
tptp_fun_X1_0: $i > $i ).
tff(multiplication_type,type,
multiplication: ( $i * $i ) > $i ).
tff(addition_type,type,
addition: ( $i * $i ) > $i ).
tff(test_type,type,
test: $i > $o ).
tff(c_type,type,
c: $i > $i ).
tff(1,plain,
^ [A: $i] :
refl(( ( multiplication(A,one) = A )
<=> ( multiplication(A,one) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i] : ( multiplication(A,one) = A )
<=> ! [A: $i] : ( multiplication(A,one) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( multiplication(A,one) = A )
<=> ! [A: $i] : ( multiplication(A,one) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: $i] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
tff(5,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( multiplication(A,one) = A )
| ( multiplication(tptp_fun_X1_0(one),one) = tptp_fun_X1_0(one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiplication(tptp_fun_X1_0(one),one) = tptp_fun_X1_0(one),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X0: $i,X1: $i] :
refl(( ~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
<=> ~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
<=> ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X0: $i,X1: $i] :
trans(trans(monotonicity(rewrite(( ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) )
<=> ~ ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) ) )),
( ( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) )
<=> ( complement(X1,X0)
<=> ~ ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) ) ) )),
rewrite(( ( complement(X1,X0)
<=> ~ ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) ) )
<=> ~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ) )),
( ( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) )
<=> ~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ) )),
rewrite(( ~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
<=> ~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ) )),
( ( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) )
<=> ~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) )
<=> ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) )
<=> ! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
^ [X0: $i,X1: $i] :
rewrite(( ( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) )
<=> ( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) )
<=> ! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
tff(18,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) ),
inference(modus_ponens,[status(thm)],[21,11]) ).
tff(23,plain,
( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one ) )
<=> complement(tptp_fun_X1_0(one),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one ) )
<=> complement(tptp_fun_X1_0(one),one) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
^ [X0: $i] :
refl(( ~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [X0: $i] :
rewrite(( ~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
^ [X0: $i] :
trans(monotonicity(rewrite(( ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) )
<=> ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )),
( ( ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
& ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ( ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
& ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) )),
rewrite(( ( ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
& ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) )),
( ( ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
& ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X0: $i] :
( ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
& ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
<=> ! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X0: $i] :
( test(X0)
<=> ? [X1: $i] : complement(X1,X0) )
<=> ! [X0: $i] :
( test(X0)
<=> ? [X1: $i] : complement(X1,X0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [X0: $i] :
( test(X0)
<=> ? [X1: $i] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
tff(34,plain,
! [X0: $i] :
( test(X0)
<=> ? [X1: $i] : complement(X1,X0) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X0: $i] :
( ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
& ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ~ ! [X0: $i] :
~ ( ~ ( ~ test(X0)
| complement(tptp_fun_X1_0(X0),X0) )
| ~ ( test(X0)
| ! [X1: $i] : ~ complement(X1,X0) ) )
| ~ ( ~ ( ~ test(one)
| complement(tptp_fun_X1_0(one),one) )
| ~ ( test(one)
| ! [X1: $i] : ~ complement(X1,one) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
~ ( ~ ( ~ test(one)
| complement(tptp_fun_X1_0(one),one) )
| ~ ( test(one)
| ! [X1: $i] : ~ complement(X1,one) ) ),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ( ~ test(one)
| complement(tptp_fun_X1_0(one),one) )
| ~ ( test(one)
| ! [X1: $i] : ~ complement(X1,one) )
| ~ test(one)
| complement(tptp_fun_X1_0(one),one) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
( ~ test(one)
| complement(tptp_fun_X1_0(one),one) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ( c(one) != zero )
<=> ( c(one) != zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
c(one) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(44,plain,
c(one) != zero,
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
^ [X0: $i] :
refl(( ( test(X0)
| ( c(X0) = zero ) )
<=> ( test(X0)
| ( c(X0) = zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) )
<=> ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) )
<=> ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
^ [X0: $i] :
rewrite(( ( ~ test(X0)
=> ( c(X0) = zero ) )
<=> ( test(X0)
| ( c(X0) = zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [X0: $i] :
( ~ test(X0)
=> ( c(X0) = zero ) )
<=> ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [X0: $i] :
( ~ test(X0)
=> ( c(X0) = zero ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_4) ).
tff(51,plain,
! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) )
| test(one)
| ( c(one) = zero ) )
<=> ( ~ ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) )
| test(one)
| ( c(one) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) )
| test(one)
| ( c(one) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) )
| test(one)
| ( c(one) = zero ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
test(one),
inference(unit_resolution,[status(thm)],[57,54,44]) ).
tff(59,plain,
( ~ ( ~ test(one)
| complement(tptp_fun_X1_0(one),one) )
| ~ test(one)
| complement(tptp_fun_X1_0(one),one) ),
inference(tautology,[status(thm)],[]) ).
tff(60,plain,
( ~ ( ~ test(one)
| complement(tptp_fun_X1_0(one),one) )
| complement(tptp_fun_X1_0(one),one) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
complement(tptp_fun_X1_0(one),one),
inference(unit_resolution,[status(thm)],[60,41]) ).
tff(62,plain,
( ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one ) )
<=> complement(tptp_fun_X1_0(one),one) )
| ~ ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one ) )
| ~ complement(tptp_fun_X1_0(one),one) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
( ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one ) )
<=> complement(tptp_fun_X1_0(one),one) )
| ~ ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one ) ) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
~ ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one ) ),
inference(unit_resolution,[status(thm)],[63,24]) ).
tff(65,plain,
( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one )
| ( multiplication(tptp_fun_X1_0(one),one) = zero ) ),
inference(tautology,[status(thm)],[]) ).
tff(66,plain,
multiplication(tptp_fun_X1_0(one),one) = zero,
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
zero = multiplication(tptp_fun_X1_0(one),one),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
zero = tptp_fun_X1_0(one),
inference(transitivity,[status(thm)],[67,9]) ).
tff(69,plain,
( complement(one,zero)
<=> complement(one,tptp_fun_X1_0(one)) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( complement(one,tptp_fun_X1_0(one))
<=> complement(one,zero) ),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) )
<=> ( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) )
<=> ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ( ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) )
<=> ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ~ ( ( ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) )
<=> ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ~ ( ( ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) )
<=> ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) )
<=> ( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) )
<=> ( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ) ),
inference(transitivity,[status(thm)],[76,71]) ).
tff(78,plain,
( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [X0: $i,X1: $i] :
~ ( ( ( multiplication(X0,X1) != zero )
| ( multiplication(X1,X0) != zero )
| ( addition(X0,X1) != one ) )
<=> complement(X1,X0) )
| ~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
~ ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) ),
inference(unit_resolution,[status(thm)],[79,22]) ).
tff(81,plain,
( ( addition(tptp_fun_X1_0(one),one) = addition(one,tptp_fun_X1_0(one)) )
<=> ( addition(one,tptp_fun_X1_0(one)) = addition(tptp_fun_X1_0(one),one) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(82,plain,
( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one )
| ( addition(one,tptp_fun_X1_0(one)) = one ) ),
inference(tautology,[status(thm)],[]) ).
tff(83,plain,
addition(one,tptp_fun_X1_0(one)) = one,
inference(unit_resolution,[status(thm)],[82,64]) ).
tff(84,plain,
one = addition(one,tptp_fun_X1_0(one)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ( addition(tptp_fun_X1_0(one),one) = one )
<=> ( addition(tptp_fun_X1_0(one),one) = addition(one,tptp_fun_X1_0(one)) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ( addition(tptp_fun_X1_0(one),one) = one )
<=> ( addition(one,tptp_fun_X1_0(one)) = addition(tptp_fun_X1_0(one),one) ) ),
inference(transitivity,[status(thm)],[85,81]) ).
tff(87,plain,
( ( addition(one,tptp_fun_X1_0(one)) = addition(tptp_fun_X1_0(one),one) )
<=> ( addition(tptp_fun_X1_0(one),one) = one ) ),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
^ [A: $i,B: $i] :
refl(( ( addition(A,B) = addition(B,A) )
<=> ( addition(A,B) = addition(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(92,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,tptp_fun_X1_0(one)) = addition(tptp_fun_X1_0(one),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
addition(one,tptp_fun_X1_0(one)) = addition(tptp_fun_X1_0(one),one),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
addition(tptp_fun_X1_0(one),one) = one,
inference(modus_ponens,[status(thm)],[96,87]) ).
tff(98,plain,
( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(one,tptp_fun_X1_0(one)) != one )
| ( multiplication(one,tptp_fun_X1_0(one)) = zero ) ),
inference(tautology,[status(thm)],[]) ).
tff(99,plain,
multiplication(one,tptp_fun_X1_0(one)) = zero,
inference(unit_resolution,[status(thm)],[98,64]) ).
tff(100,plain,
( ~ ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
| ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) ),
inference(tautology,[status(thm)],[]) ).
tff(101,plain,
( ~ ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
| ( addition(tptp_fun_X1_0(one),one) != one ) ),
inference(unit_resolution,[status(thm)],[100,99,66]) ).
tff(102,plain,
~ ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) ),
inference(unit_resolution,[status(thm)],[101,97]) ).
tff(103,plain,
( ( ( ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one ) )
<=> complement(one,tptp_fun_X1_0(one)) )
| ( multiplication(one,tptp_fun_X1_0(one)) != zero )
| ( multiplication(tptp_fun_X1_0(one),one) != zero )
| ( addition(tptp_fun_X1_0(one),one) != one )
| complement(one,tptp_fun_X1_0(one)) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
complement(one,tptp_fun_X1_0(one)),
inference(unit_resolution,[status(thm)],[103,102,80]) ).
tff(105,plain,
complement(one,zero),
inference(modus_ponens,[status(thm)],[104,70]) ).
tff(106,plain,
^ [X0: $i,X1: $i] :
refl(( ( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
<=> ( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
<=> ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
<=> ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
^ [X0: $i,X1: $i] :
rewrite(( ( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
<=> ( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [X0: $i,X1: $i] :
( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
<=> ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [X0: $i,X1: $i] :
( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
tff(112,plain,
! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
| ~ test(one)
| ( ( c(one) = zero )
<=> complement(one,zero) ) )
<=> ( ~ ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
| ~ test(one)
| ( ( c(one) = zero )
<=> complement(one,zero) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
| ~ test(one)
| ( ( c(one) = zero )
<=> complement(one,zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [X0: $i,X1: $i] :
( ~ test(X0)
| ( ( c(X0) = X1 )
<=> complement(X0,X1) ) )
| ~ test(one)
| ( ( c(one) = zero )
<=> complement(one,zero) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( ( c(one) = zero )
<=> complement(one,zero) ),
inference(unit_resolution,[status(thm)],[118,115,58]) ).
tff(120,plain,
( ~ ( ( c(one) = zero )
<=> complement(one,zero) )
| ( c(one) = zero )
| ~ complement(one,zero) ),
inference(tautology,[status(thm)],[]) ).
tff(121,plain,
( ~ ( ( c(one) = zero )
<=> complement(one,zero) )
| ~ complement(one,zero) ),
inference(unit_resolution,[status(thm)],[120,44]) ).
tff(122,plain,
~ complement(one,zero),
inference(unit_resolution,[status(thm)],[121,119]) ).
tff(123,plain,
$false,
inference(unit_resolution,[status(thm)],[122,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE005+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 18:49:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------