%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN158-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:22 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 70
% Syntax : Number of formulae : 154 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 795 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1135 ( 530 ~; 526 |; 0 &)
% ( 79 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 36 ( 36 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 318 ( 288 !; 0 ?; 318 :)
% Comments :
%------------------------------------------------------------------------------
tff(q4_type,type,
q4: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
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(s0_type,type,
s0: $i > $o ).
tff(d_type,type,
d: $i ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(k3_type,type,
k3: ( $i * $i * $i ) > $o ).
tff(r2_type,type,
r2: $i > $o ).
tff(r1_type,type,
r1: $i > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(n5_type,type,
n5: ( $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_238) ).
tff(5,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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(12,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(17,plain,
l0(a),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( s0(d)
<=> s0(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(20,plain,
s0(d),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( m1(a,a,a)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,axiom,
( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_023) ).
tff(27,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[27,21]) ).
tff(29,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[29,21]) ).
tff(31,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[30,21]) ).
tff(32,plain,
m1(a,a,a),
inference(unit_resolution,[status(thm)],[31,20,17]) ).
tff(33,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
p2(a,a,a),
inference(unit_resolution,[status(thm)],[35,32,14]) ).
tff(37,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
m3(a,a,a),
inference(unit_resolution,[status(thm)],[42,36,7]) ).
tff(44,plain,
^ [I: $i] :
refl(( ( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ( q2(I,I,I)
| ~ p1(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_181) ).
tff(48,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( p1(a,a,a)
| ~ l0(a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_088) ).
tff(54,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[54,51]) ).
tff(56,plain,
p1(a,a,a),
inference(unit_resolution,[status(thm)],[55,17]) ).
tff(57,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(a,a,a)
| q2(a,a,a) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(a,a,a)
| q2(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( q2(a,a,a)
| ~ p1(a,a,a) )
<=> ( ~ p1(a,a,a)
| q2(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(a,a,a)
| ~ p1(a,a,a) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(a,a,a)
| q2(a,a,a) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(a,a,a)
| ~ p1(a,a,a) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(a,a,a)
| q2(a,a,a) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(a,a,a)
| ~ p1(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(a,a,a)
| q2(a,a,a) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
q2(a,a,a),
inference(unit_resolution,[status(thm)],[62,56,50]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,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(68,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)],[67]) ).
tff(69,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(70,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)],[69,68]) ).
tff(71,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)],[70,66]) ).
tff(72,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)],[71]) ).
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) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
^ [B: $i,A: $i,J: $i,C: $i] :
refl(( ( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
<=> ( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
<=> ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
<=> ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [B: $i,A: $i,J: $i,C: $i] :
trans(monotonicity(rewrite(( ( q1(J,A,J)
| ~ n0(B,A) )
<=> ( ~ n0(B,A)
| q1(J,A,J) ) )),
( ( q1(J,A,J)
| ~ n0(B,A)
| ~ p0(C,J) )
<=> ( ~ n0(B,A)
| q1(J,A,J)
| ~ p0(C,J) ) )),
rewrite(( ( ~ n0(B,A)
| q1(J,A,J)
| ~ p0(C,J) )
<=> ( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) )),
( ( q1(J,A,J)
| ~ n0(B,A)
| ~ p0(C,J) )
<=> ( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [B: $i,A: $i,J: $i,C: $i] :
( q1(J,A,J)
| ~ n0(B,A)
| ~ p0(C,J) )
<=> ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [B: $i,A: $i,J: $i,C: $i] :
( q1(J,A,J)
| ~ n0(B,A)
| ~ p0(C,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_092) ).
tff(80,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(86,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( n0(d,b)
<=> n0(d,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
n0(d,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_7) ).
tff(89,plain,
n0(d,b),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(b,d)
| ~ n0(d,b)
| q1(d,b,d) )
<=> ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(b,d)
| ~ n0(d,b)
| q1(d,b,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(b,d)
| ~ n0(d,b)
| q1(d,b,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(b,d)
| ~ n0(d,b)
| q1(d,b,d) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
q1(d,b,d),
inference(unit_resolution,[status(thm)],[92,89,86,83]) ).
tff(94,plain,
^ [D: $i,E: $i] :
refl(( ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
^ [D: $i,E: $i] :
trans(monotonicity(rewrite(( ( r1(D)
| ~ q0(D,E)
| ~ s0(d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| r1(D) ) )),
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| r1(D)
| ~ q1(d,E,d) ) )),
rewrite(( ( ~ q0(D,E)
| ~ s0(d)
| r1(D)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [D: $i,E: $i] :
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [D: $i,E: $i] :
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_124) ).
tff(100,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( q0(a,b)
<=> q0(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,axiom,
q0(a,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_36) ).
tff(106,plain,
q0(a,b),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( ~ q0(a,b)
| ~ s0(d)
| ~ q1(d,b,d)
| r1(a) )
<=> ( ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(a,b)
| ~ s0(d)
| ~ q1(d,b,d)
| r1(a) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(a,b)
| ~ s0(d)
| ~ q1(d,b,d)
| r1(a) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(a,b)
| ~ s0(d)
| ~ q1(d,b,d)
| r1(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
r1(a),
inference(unit_resolution,[status(thm)],[112,20,106,103,93]) ).
tff(114,plain,
^ [G: $i] :
refl(( ( ~ l0(G)
| ~ r1(G)
| r2(G) )
<=> ( ~ l0(G)
| ~ r1(G)
| r2(G) ) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
<=> ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
( ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
<=> ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
^ [G: $i] :
rewrite(( ( r2(G)
| ~ r1(G)
| ~ l0(G) )
<=> ( ~ l0(G)
| ~ r1(G)
| r2(G) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [G: $i] :
( r2(G)
| ~ r1(G)
| ~ l0(G) )
<=> ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,axiom,
! [G: $i] :
( r2(G)
| ~ r1(G)
| ~ l0(G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_188) ).
tff(120,plain,
! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,plain,
( ( ~ ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
| ~ l0(a)
| ~ r1(a)
| r2(a) )
<=> ( ~ ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
| ~ l0(a)
| ~ r1(a)
| r2(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
| ~ l0(a)
| ~ r1(a)
| r2(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
| ~ l0(a)
| ~ r1(a)
| r2(a) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
r2(a),
inference(unit_resolution,[status(thm)],[126,17,123,113]) ).
tff(128,plain,
( ( ~ r2(a)
| k3(a,a,a) )
<=> ( ~ r2(a)
| k3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
( ( k3(a,a,a)
| ~ r2(a) )
<=> ( ~ r2(a)
| k3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,axiom,
( k3(a,a,a)
| ~ r2(a) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_204) ).
tff(131,plain,
( ~ r2(a)
| k3(a,a,a) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
( ~ r2(a)
| k3(a,a,a) ),
inference(modus_ponens,[status(thm)],[131,128]) ).
tff(133,plain,
k3(a,a,a),
inference(unit_resolution,[status(thm)],[132,127]) ).
tff(134,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) )
| ~ k3(a,a,a)
| ~ q2(a,a,a)
| ~ m3(a,a,a)
| q4(a,a) )
<=> ( ~ ! [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) )
| ~ k3(a,a,a)
| ~ q2(a,a,a)
| ~ m3(a,a,a)
| q4(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( ~ m3(a,a,a)
| ~ q2(a,a,a)
| ~ k3(a,a,a)
| q4(a,a) )
<=> ( ~ k3(a,a,a)
| ~ q2(a,a,a)
| ~ m3(a,a,a)
| q4(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,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(a,a,a)
| ~ q2(a,a,a)
| ~ k3(a,a,a)
| q4(a,a) )
<=> ( ~ ! [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) )
| ~ k3(a,a,a)
| ~ q2(a,a,a)
| ~ m3(a,a,a)
| q4(a,a) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,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(a,a,a)
| ~ q2(a,a,a)
| ~ k3(a,a,a)
| q4(a,a) )
<=> ( ~ ! [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) )
| ~ k3(a,a,a)
| ~ q2(a,a,a)
| ~ m3(a,a,a)
| q4(a,a) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,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(a,a,a)
| ~ q2(a,a,a)
| ~ k3(a,a,a)
| q4(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,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) )
| ~ k3(a,a,a)
| ~ q2(a,a,a)
| ~ m3(a,a,a)
| q4(a,a) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
q4(a,a),
inference(unit_resolution,[status(thm)],[139,133,73,63,43]) ).
tff(141,plain,
( ~ n5(a,a)
<=> ~ n5(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,axiom,
~ n5(a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(143,plain,
~ n5(a,a),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
^ [D: $i,C: $i] :
refl(( ( n5(C,C)
| ~ q4(D,C) )
<=> ( n5(C,C)
| ~ q4(D,C) ) )),
inference(bind,[status(th)],[]) ).
tff(145,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)],[144]) ).
tff(146,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(147,axiom,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_313) ).
tff(148,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
( ( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(a,a)
| ~ q4(a,a) )
<=> ( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(a,a)
| ~ q4(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(a,a)
| ~ q4(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(a,a)
| ~ q4(a,a) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
$false,
inference(unit_resolution,[status(thm)],[153,150,143,140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN158-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:30:42 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------