%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN113-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:38:16 AM UTC 2025
% Result : Unsatisfiable 0.46s 0.63s
% Output : Proof 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 83 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 388 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 523 ( 243 ~; 238 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 179 ( 159 !; 0 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(d_type,type,
d: $i ).
tff(k2_type,type,
k2: ( $i * $i ) > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [A: $i,J: $i] :
refl(( ( ~ q1(A,J,J)
| k2(J,J) )
<=> ( ~ q1(A,J,J)
| k2(J,J) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [A: $i,J: $i] :
rewrite(( ( k2(J,J)
| ~ q1(A,J,J) )
<=> ( ~ q1(A,J,J)
| k2(J,J) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_129) ).
tff(7,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(13,plain,
k0(e),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( s0(d)
<=> s0(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
s0(d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(16,plain,
s0(d),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( q1(d,d,d)
| ~ k0(e) )
<=> ( ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(transitivity,[status(thm)],[20,18]) ).
tff(22,axiom,
( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_117) ).
tff(23,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[23,17]) ).
tff(25,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[25,17]) ).
tff(27,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[26,17]) ).
tff(28,plain,
q1(d,d,d),
inference(unit_resolution,[status(thm)],[27,16,13]) ).
tff(29,plain,
( ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) )
<=> ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
k2(d,d),
inference(unit_resolution,[status(thm)],[31,28,10]) ).
tff(33,plain,
( ~ k2(e,d)
<=> ~ k2(e,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
~ k2(e,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(35,plain,
~ k2(e,d),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(40,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( n0(c,d)
<=> n0(c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
n0(c,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
tff(45,plain,
n0(c,d),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
k1(d),
inference(unit_resolution,[status(thm)],[48,45,42]) ).
tff(50,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
refl(( ( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
<=> ( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( k2(C,D)
| ~ m1(E,D,C) )
<=> ( ~ m1(E,D,C)
| k2(C,D) ) )),
( ( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F) )
<=> ( ~ m1(E,D,C)
| k2(C,D)
| ~ k1(F) ) )),
rewrite(( ( ~ m1(E,D,C)
| k2(C,D)
| ~ k1(F) )
<=> ( ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ) )),
( ( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F) )
<=> ( ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ) )),
( ( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) )
<=> ( ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D)
| ~ k2(F,D) ) )),
rewrite(( ( ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D)
| ~ k2(F,D) )
<=> ( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) )),
( ( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) )
<=> ( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [D: $i,E: $i,F: $i,C: $i] :
( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_127) ).
tff(56,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(d)
| ~ k2(d,d)
| ~ m1(e,d,e)
| k2(e,d) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(d)
| ~ k2(d,d)
| ~ m1(e,d,e)
| k2(e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(d)
| ~ k2(d,d)
| ~ m1(e,d,e)
| k2(e,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(d)
| ~ k2(d,d)
| ~ m1(e,d,e)
| k2(e,d) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ m1(e,d,e),
inference(unit_resolution,[status(thm)],[62,59,49,35,32]) ).
tff(64,plain,
^ [I: $i,H: $i,G: $i] :
refl(( ( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) )
<=> ( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
^ [I: $i,H: $i,G: $i] :
trans(monotonicity(rewrite(( ( m1(G,H,G)
| ~ p0(I,H) )
<=> ( ~ p0(I,H)
| m1(G,H,G) ) )),
( ( m1(G,H,G)
| ~ p0(I,H)
| ~ r0(G) )
<=> ( ~ p0(I,H)
| m1(G,H,G)
| ~ r0(G) ) )),
rewrite(( ( ~ p0(I,H)
| m1(G,H,G)
| ~ r0(G) )
<=> ( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ) )),
( ( m1(G,H,G)
| ~ p0(I,H)
| ~ r0(G) )
<=> ( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [I: $i,H: $i,G: $i] :
( m1(G,H,G)
| ~ p0(I,H)
| ~ r0(G) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [I: $i,H: $i,G: $i] :
( m1(G,H,G)
| ~ p0(I,H)
| ~ r0(G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_007) ).
tff(70,plain,
! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(76,plain,
r0(e),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
p0(b,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(79,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) )
| ~ r0(e)
| ~ p0(b,d)
| m1(e,d,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) )
| ~ r0(e)
| ~ p0(b,d)
| m1(e,d,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) )
| ~ r0(e)
| ~ p0(b,d)
| m1(e,d,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) )
| ~ r0(e)
| ~ p0(b,d)
| m1(e,d,e) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
$false,
inference(unit_resolution,[status(thm)],[82,79,76,73,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN113-1 : TPTP v9.0.0. Released v1.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:28:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.46/0.63 % SZS status Unsatisfiable
% 0.46/0.63 % SZS output start Proof
% See solution above
% 0.47/0.65 % E exiting
%------------------------------------------------------------------------------