%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN161-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:38:23 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 55
% Syntax : Number of formulae : 122 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 563 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 775 ( 363 ~; 351 |; 0 &)
% ( 61 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 286 ( 260 !; 0 ?; 286 :)
% Comments :
%------------------------------------------------------------------------------
tff(n5_type,type,
n5: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(q4_type,type,
q4: ( $i * $i ) > $o ).
tff(m3_type,type,
m3: ( $i * $i * $i ) > $o ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(k3_type,type,
k3: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [D: $i,E: $i] :
refl(( ( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ( p2(D,E,D)
| ~ m1(E,D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(5,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( l0(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(10,plain,
l0(c),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ l0(c)
| m1(c,c,c) )
<=> ( ~ l0(c)
| m1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( m1(c,c,c)
| ~ l0(c) )
<=> ( ~ l0(c)
| m1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
( m1(c,c,c)
| ~ l0(c) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_020) ).
tff(14,plain,
( ~ l0(c)
| m1(c,c,c) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ~ l0(c)
| m1(c,c,c) ),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
m1(c,c,c),
inference(unit_resolution,[status(thm)],[15,10]) ).
tff(17,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
p2(c,c,c),
inference(unit_resolution,[status(thm)],[22,16,7]) ).
tff(24,plain,
^ [I: $i] :
refl(( ( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ( m3(I,I,I)
| ~ p2(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_238) ).
tff(28,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(c,c,c)
| m3(c,c,c) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(c,c,c)
| m3(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( m3(c,c,c)
| ~ p2(c,c,c) )
<=> ( ~ p2(c,c,c)
| m3(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(c,c,c)
| ~ p2(c,c,c) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(c,c,c)
| m3(c,c,c) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(c,c,c)
| ~ p2(c,c,c) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(c,c,c)
| m3(c,c,c) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(c,c,c)
| ~ p2(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(c,c,c)
| m3(c,c,c) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
m3(c,c,c),
inference(unit_resolution,[status(thm)],[36,30,23]) ).
tff(38,plain,
^ [A: $i,J: $i] :
refl(( ( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) )
<=> ( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) )
<=> ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) )
<=> ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [A: $i,J: $i] :
trans(monotonicity(rewrite(( ( q2(J,J,J)
| ~ k1(A) )
<=> ( ~ k1(A)
| q2(J,J,J) ) )),
( ( q2(J,J,J)
| ~ k1(A)
| ~ n1(J,J,A) )
<=> ( ~ k1(A)
| q2(J,J,J)
| ~ n1(J,J,A) ) )),
rewrite(( ( ~ k1(A)
| q2(J,J,J)
| ~ n1(J,J,A) )
<=> ( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ) )),
( ( q2(J,J,J)
| ~ k1(A)
| ~ n1(J,J,A) )
<=> ( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [A: $i,J: $i] :
( q2(J,J,J)
| ~ k1(A)
| ~ n1(J,J,A) )
<=> ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [A: $i,J: $i] :
( q2(J,J,J)
| ~ k1(A)
| ~ n1(J,J,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_179) ).
tff(44,plain,
! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(52,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(57,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
k1(c),
inference(unit_resolution,[status(thm)],[60,57,54]) ).
tff(62,plain,
( ( ~ l0(c)
| n1(c,c,c) )
<=> ( ~ l0(c)
| n1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( n1(c,c,c)
| ~ l0(c) )
<=> ( ~ l0(c)
| n1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
( n1(c,c,c)
| ~ l0(c) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_049) ).
tff(65,plain,
( ~ l0(c)
| n1(c,c,c) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ l0(c)
| n1(c,c,c) ),
inference(modus_ponens,[status(thm)],[65,62]) ).
tff(67,plain,
n1(c,c,c),
inference(unit_resolution,[status(thm)],[66,10]) ).
tff(68,plain,
( ( ~ ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) )
| ~ k1(c)
| ~ n1(c,c,c)
| q2(c,c,c) )
<=> ( ~ ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) )
| ~ k1(c)
| ~ n1(c,c,c)
| q2(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) )
| ~ k1(c)
| ~ n1(c,c,c)
| q2(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [A: $i,J: $i] :
( ~ k1(A)
| ~ n1(J,J,A)
| q2(J,J,J) )
| ~ k1(c)
| ~ n1(c,c,c)
| q2(c,c,c) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
q2(c,c,c),
inference(unit_resolution,[status(thm)],[70,67,61,47]) ).
tff(72,plain,
^ [B: $i,D: $i,E: $i,F: $i,C: $i] :
refl(( ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [B: $i,D: $i,E: $i,F: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( q4(B,C)
| ~ k3(D,D,B) )
<=> ( ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B) )
<=> ( ~ k3(D,D,B)
| q4(B,C)
| ~ q2(E,C,B) ) )),
rewrite(( ( ~ k3(D,D,B)
| q4(B,C)
| ~ q2(E,C,B) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C)
| ~ m3(E,F,E) ) )),
rewrite(( ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C)
| ~ m3(E,F,E) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_295) ).
tff(78,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
^ [D: $i,C: $i] :
refl(( ( ~ p2(D,C,C)
| k3(C,D,C) )
<=> ( ~ p2(D,C,C)
| k3(C,D,C) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
<=> ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
<=> ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [D: $i,C: $i] :
rewrite(( ( k3(C,D,C)
| ~ p2(D,C,C) )
<=> ( ~ p2(D,C,C)
| k3(C,D,C) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [D: $i,C: $i] :
( k3(C,D,C)
| ~ p2(D,C,C) )
<=> ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [D: $i,C: $i] :
( k3(C,D,C)
| ~ p2(D,C,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_206) ).
tff(88,plain,
! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
| ~ p2(c,c,c)
| k3(c,c,c) )
<=> ( ~ ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
| ~ p2(c,c,c)
| k3(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
| ~ p2(c,c,c)
| k3(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
| ~ p2(c,c,c)
| k3(c,c,c) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
k3(c,c,c),
inference(unit_resolution,[status(thm)],[94,91,23]) ).
tff(96,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| ~ m3(c,c,c)
| q4(c,c) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| ~ m3(c,c,c)
| q4(c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ( ~ m3(c,c,c)
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| q4(c,c) )
<=> ( ~ q2(c,c,c)
| ~ k3(c,c,c)
| ~ m3(c,c,c)
| q4(c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(c,c,c)
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| q4(c,c) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| ~ m3(c,c,c)
| q4(c,c) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(c,c,c)
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| q4(c,c) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| ~ m3(c,c,c)
| q4(c,c) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(c,c,c)
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| q4(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ q2(c,c,c)
| ~ k3(c,c,c)
| ~ m3(c,c,c)
| q4(c,c) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
q4(c,c),
inference(unit_resolution,[status(thm)],[101,95,81,71,37]) ).
tff(103,plain,
^ [D: $i,C: $i] :
refl(( ( n5(C,C)
| ~ q4(D,C) )
<=> ( n5(C,C)
| ~ q4(D,C) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
<=> ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
<=> ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_313) ).
tff(107,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
( ( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(c,c)
| ~ q4(c,c) )
<=> ( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(c,c)
| ~ q4(c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(c,c)
| ~ q4(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(c,c)
| ~ q4(c,c) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
n5(c,c),
inference(unit_resolution,[status(thm)],[112,109,102]) ).
tff(114,plain,
^ [X: $i] :
refl(( ~ n5(c,X)
<=> ~ n5(c,X) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [X: $i] : ~ n5(c,X)
<=> ! [X: $i] : ~ n5(c,X) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
( ! [X: $i] : ~ n5(c,X)
<=> ! [X: $i] : ~ n5(c,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
! [X: $i] : ~ n5(c,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(118,plain,
! [X: $i] : ~ n5(c,X),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [X: $i] : ~ n5(c,X),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [X: $i] : ~ n5(c,X),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
( ~ ! [X: $i] : ~ n5(c,X)
| ~ n5(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
$false,
inference(unit_resolution,[status(thm)],[121,120,113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN161-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:28:37 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------