%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN117-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:38:17 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.45s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 63
% Syntax : Number of formulae : 142 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 605 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 827 ( 383 ~; 379 |; 0 &)
% ( 65 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 348 ( 315 !; 0 ?; 348 :)
% Comments :
%------------------------------------------------------------------------------
tff(r3_type,type,
r3: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(k5_type,type,
k5: $i > $o ).
tff(s4_type,type,
s4: $i > $o ).
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(n2_type,type,
n2: $i > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(l1_type,type,
l1: ( $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,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(10,plain,
r0(e),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(14,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
m1(e,e,e),
inference(unit_resolution,[status(thm)],[15,10]) ).
tff(17,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[22,16,7]) ).
tff(24,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ( ~ p2(B,D,C)
| r3(B,C,B) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [B: $i,D: $i,C: $i] :
rewrite(( ( r3(B,C,B)
| ~ p2(B,D,C) )
<=> ( ~ p2(B,D,C)
| r3(B,C,B) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [B: $i,D: $i,C: $i] :
( r3(B,C,B)
| ~ p2(B,D,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [B: $i,D: $i,C: $i] :
( r3(B,C,B)
| ~ p2(B,D,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_267) ).
tff(30,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(e,e,e)
| r3(e,e,e) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(e,e,e)
| r3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(e,e,e)
| r3(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(e,e,e)
| r3(e,e,e) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
r3(e,e,e),
inference(unit_resolution,[status(thm)],[36,33,23]) ).
tff(38,plain,
( ~ k5(e)
<=> ~ k5(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
~ k5(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(40,plain,
~ k5(e),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( n2(A)
| ~ p1(B,C,A) )
<=> ( n2(A)
| ~ p1(B,C,A) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(45,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(50,plain,
k0(e),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(57,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[57,51]) ).
tff(59,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[59,51]) ).
tff(61,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[60,51]) ).
tff(62,plain,
p1(e,e,e),
inference(unit_resolution,[status(thm)],[61,10,50]) ).
tff(63,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
n2(e),
inference(unit_resolution,[status(thm)],[65,62,47]) ).
tff(67,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(71,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( n0(d,e)
<=> n0(d,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
n0(d,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_3) ).
tff(76,plain,
n0(d,e),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(e)
| ~ n0(d,e) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(e)
| ~ n0(d,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(e)
| ~ n0(d,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(e)
| ~ n0(d,e) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
k1(e),
inference(unit_resolution,[status(thm)],[79,76,73]) ).
tff(81,plain,
^ [H: $i] :
refl(( ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
^ [H: $i] :
trans(monotonicity(rewrite(( ( p3(H,H,H)
| ~ k1(H) )
<=> ( ~ k1(H)
| p3(H,H,H) ) )),
( ( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ( ~ k1(H)
| p3(H,H,H)
| ~ n2(H) ) )),
rewrite(( ( ~ k1(H)
| p3(H,H,H)
| ~ n2(H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
( ( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_249) ).
tff(87,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(e)
| ~ n2(e)
| p3(e,e,e) )
<=> ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(e)
| ~ n2(e)
| p3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(e)
| ~ n2(e)
| p3(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(e)
| ~ n2(e)
| p3(e,e,e) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
p3(e,e,e),
inference(unit_resolution,[status(thm)],[93,90,80,66]) ).
tff(95,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
rewrite(( ( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) )
<=> ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_299) ).
tff(101,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[103,96]) ).
tff(105,plain,
^ [H: $i,G: $i] :
refl(( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
^ [H: $i,G: $i] :
rewrite(( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(111,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
l1(e,e),
inference(unit_resolution,[status(thm)],[117,76,114]) ).
tff(119,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(e,e)
| s4(e)
| ~ p3(e,e,e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(e,e)
| s4(e)
| ~ p3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ( ~ l1(e,e)
| ~ p3(e,e,e)
| s4(e) )
<=> ( ~ l1(e,e)
| s4(e)
| ~ p3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(e,e)
| ~ p3(e,e,e)
| s4(e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(e,e)
| s4(e)
| ~ p3(e,e,e) ) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(e,e)
| ~ p3(e,e,e)
| s4(e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(e,e)
| s4(e)
| ~ p3(e,e,e) ) ),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(e,e)
| ~ p3(e,e,e)
| s4(e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(e,e)
| s4(e)
| ~ p3(e,e,e) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
s4(e),
inference(unit_resolution,[status(thm)],[124,118,104,94]) ).
tff(126,plain,
^ [E: $i,F: $i,G: $i] :
refl(( ( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
<=> ( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
<=> ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
<=> ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
^ [E: $i,F: $i,G: $i] :
rewrite(( ( k5(E)
| ~ s4(F)
| ~ r3(G,E,E) )
<=> ( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [E: $i,F: $i,G: $i] :
( k5(E)
| ~ s4(F)
| ~ r3(G,E,E) )
<=> ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,axiom,
! [E: $i,F: $i,G: $i] :
( k5(E)
| ~ s4(F)
| ~ r3(G,E,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_300) ).
tff(132,plain,
! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) ),
inference(modus_ponens,[status(thm)],[134,127]) ).
tff(136,plain,
( ( ~ ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
| ~ s4(e)
| k5(e)
| ~ r3(e,e,e) )
<=> ( ~ ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
| ~ s4(e)
| k5(e)
| ~ r3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ( ~ r3(e,e,e)
| ~ s4(e)
| k5(e) )
<=> ( ~ s4(e)
| k5(e)
| ~ r3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
( ( ~ ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
| ~ r3(e,e,e)
| ~ s4(e)
| k5(e) )
<=> ( ~ ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
| ~ s4(e)
| k5(e)
| ~ r3(e,e,e) ) ),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ( ~ ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
| ~ r3(e,e,e)
| ~ s4(e)
| k5(e) )
<=> ( ~ ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
| ~ s4(e)
| k5(e)
| ~ r3(e,e,e) ) ),
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,plain,
( ~ ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
| ~ r3(e,e,e)
| ~ s4(e)
| k5(e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [E: $i,F: $i,G: $i] :
( ~ r3(G,E,E)
| ~ s4(F)
| k5(E) )
| ~ s4(e)
| k5(e)
| ~ r3(e,e,e) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
$false,
inference(unit_resolution,[status(thm)],[141,135,125,40,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN117-1 : TPTP v9.0.0. Released v1.1.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n006.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 12:28:20 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.45 % SZS status Unsatisfiable
% 0.18/0.45 % SZS output start Proof
% See solution above
% 0.18/0.47 % E exiting
%------------------------------------------------------------------------------