%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN109-1 : 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 05:38:16 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 40
% Syntax : Number of formulae : 85 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 416 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 567 ( 263 ~; 259 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 221 ( 197 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(k2_type,type,
k2: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(e_type,type,
e: $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(p0_type,type,
p0: ( $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(1,plain,
^ [I: $i,A: $i,J: $i] :
refl(( ( ~ m0(J,A,I)
| q1(I,I,I) )
<=> ( ~ m0(J,A,I)
| q1(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [I: $i,A: $i,J: $i] :
rewrite(( ( q1(I,I,I)
| ~ m0(J,A,I) )
<=> ( ~ m0(J,A,I)
| q1(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [I: $i,A: $i,J: $i] :
( q1(I,I,I)
| ~ m0(J,A,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [I: $i,A: $i,J: $i] :
( q1(I,I,I)
| ~ m0(J,A,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_121) ).
tff(7,plain,
! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
m0(e,b,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(13,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
| ~ m0(e,b,c)
| q1(c,c,c) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
| ~ m0(e,b,c)
| q1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
| ~ m0(e,b,c)
| q1(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
| ~ m0(e,b,c)
| q1(c,c,c) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
q1(c,c,c),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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(22,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)],[21]) ).
tff(23,axiom,
! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_129) ).
tff(24,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(c,c,c)
| k2(c,c) )
<=> ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(c,c,c)
| k2(c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(c,c,c)
| k2(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(c,c,c)
| k2(c,c) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
k2(c,c),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
^ [I: $i,H: $i] :
refl(( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [I: $i,H: $i] :
trans(monotonicity(rewrite(( ( m1(H,I,H)
| ~ p0(H,I) )
<=> ( m1(H,I,H)
| ~ p0(H,I) ) )),
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
rewrite(( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_029) ).
tff(38,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( p0(b,c)
<=> p0(b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
p0(b,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_22) ).
tff(44,plain,
p0(b,c),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( s0(b)
<=> s0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
s0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_5) ).
tff(47,plain,
s0(b),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
m1(b,c,b),
inference(unit_resolution,[status(thm)],[53,47,44,41]) ).
tff(55,plain,
( ~ k2(b,c)
<=> ~ k2(b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
~ k2(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(57,plain,
~ k2(b,c),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(62,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
n0(d,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(67,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,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(69,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
k1(c),
inference(unit_resolution,[status(thm)],[70,67,64]) ).
tff(72,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(73,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)],[72]) ).
tff(74,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(75,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(76,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)],[75]) ).
tff(77,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(78,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)],[77,76]) ).
tff(79,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)],[78,74]) ).
tff(80,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)],[79]) ).
tff(81,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)],[80,73]) ).
tff(82,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(c)
| ~ k2(c,c)
| ~ m1(b,c,b)
| k2(b,c) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(c)
| ~ k2(c,c)
| ~ m1(b,c,b)
| k2(b,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(c)
| ~ k2(c,c)
| ~ m1(b,c,b)
| k2(b,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(c)
| ~ k2(c,c)
| ~ m1(b,c,b)
| k2(b,c) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
$false,
inference(unit_resolution,[status(thm)],[84,81,71,57,54,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN109-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:28:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% See solution above
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------