%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN157-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : 11
% Number of leaves : 52
% Syntax : Number of formulae : 121 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 649 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 918 ( 432 ~; 420 |; 0 &)
% ( 66 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 42 ( 42 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 336 ( 303 !; 0 ?; 336 :)
% Comments :
%------------------------------------------------------------------------------
tff(n5_type,type,
n5: ( $i * $i ) > $o ).
tff(d_type,type,
d: $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(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(k3_type,type,
k3: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ n5(X,d)
<=> ~ n5(X,d) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ~ n5(X,d)
<=> ! [X: $i] : ~ n5(X,d) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ~ n5(X,d)
<=> ! [X: $i] : ~ n5(X,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ~ n5(X,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [X: $i] : ~ n5(X,d),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ~ n5(X,d),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ~ n5(X,d),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,axiom,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_238) ).
tff(12,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
^ [B: $i] :
refl(( ( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ( p2(B,B,B)
| ~ n1(d,d,B) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_153) ).
tff(19,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( q0(d,d)
<=> q0(d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
q0(d,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(24,plain,
q0(d,d),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(27,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[27,25]) ).
tff(29,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[30,25]) ).
tff(32,plain,
n1(d,d,d),
inference(unit_resolution,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) )
<=> ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
p2(d,d,d),
inference(unit_resolution,[status(thm)],[35,32,21]) ).
tff(37,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(d,d,d)
| m3(d,d,d) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(d,d,d)
| m3(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( m3(d,d,d)
| ~ p2(d,d,d) )
<=> ( ~ p2(d,d,d)
| m3(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(d,d,d)
| ~ p2(d,d,d) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(d,d,d)
| m3(d,d,d) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(d,d,d)
| ~ p2(d,d,d) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(d,d,d)
| m3(d,d,d) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(d,d,d)
| ~ p2(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(d,d,d)
| m3(d,d,d) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
m3(d,d,d),
inference(unit_resolution,[status(thm)],[42,36,14]) ).
tff(44,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [B: $i,D: $i,C: $i] :
trans(monotonicity(rewrite(( ( q2(B,B,B)
| ~ q0(C,B) )
<=> ( ~ q0(C,B)
| q2(B,B,B) ) )),
( ( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| q2(B,B,B)
| ~ n1(C,B,D) ) )),
rewrite(( ( ~ q0(C,B)
| q2(B,B,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
( ( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [B: $i,D: $i,C: $i] :
( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [B: $i,D: $i,C: $i] :
( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_178) ).
tff(50,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
q2(d,d,d),
inference(unit_resolution,[status(thm)],[56,24,32,53]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,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(62,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)],[61]) ).
tff(63,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(64,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)],[63,62]) ).
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) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
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) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,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)],[66,59]) ).
tff(68,plain,
^ [D: $i,E: $i,C: $i] :
refl(( ( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
<=> ( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
<=> ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
<=> ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [D: $i,E: $i,C: $i] :
trans(monotonicity(rewrite(( ( m1(C,C,C)
| ~ q0(D,E) )
<=> ( m1(C,C,C)
| ~ q0(D,E) ) )),
( ( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) )
<=> ( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) ) )),
rewrite(( ( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) )
<=> ( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) )),
( ( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) )
<=> ( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) )
<=> ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_018) ).
tff(74,plain,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( q0(e,d)
<=> q0(e,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
q0(e,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_2) ).
tff(80,plain,
q0(e,d),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( m1(d,d,d)
| ~ q0(e,d)
| ~ q0(e,d) )
<=> ( ~ q0(e,d)
| m1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| m1(d,d,d)
| ~ q0(e,d)
| ~ q0(e,d) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| m1(d,d,d)
| ~ q0(e,d)
| ~ q0(e,d) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| m1(d,d,d)
| ~ q0(e,d)
| ~ q0(e,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
m1(d,d,d),
inference(unit_resolution,[status(thm)],[86,80,77]) ).
tff(88,plain,
^ [D: $i,E: $i,C: $i] :
refl(( ( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) )
<=> ( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
^ [D: $i,E: $i,C: $i] :
trans(monotonicity(rewrite(( ( k3(C,C,C)
| ~ p2(D,E,D) )
<=> ( ~ p2(D,E,D)
| k3(C,C,C) ) )),
( ( k3(C,C,C)
| ~ p2(D,E,D)
| ~ m1(C,C,E) )
<=> ( ~ p2(D,E,D)
| k3(C,C,C)
| ~ m1(C,C,E) ) )),
rewrite(( ( ~ p2(D,E,D)
| k3(C,C,C)
| ~ m1(C,C,E) )
<=> ( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ) )),
( ( k3(C,C,C)
| ~ p2(D,E,D)
| ~ m1(C,C,E) )
<=> ( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [D: $i,E: $i,C: $i] :
( k3(C,C,C)
| ~ p2(D,E,D)
| ~ m1(C,C,E) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [D: $i,E: $i,C: $i] :
( k3(C,C,C)
| ~ p2(D,E,D)
| ~ m1(C,C,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_196) ).
tff(94,plain,
! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) )
| ~ m1(d,d,d)
| ~ p2(d,d,d)
| k3(d,d,d) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) )
| ~ m1(d,d,d)
| ~ p2(d,d,d)
| k3(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) )
| ~ m1(d,d,d)
| ~ p2(d,d,d)
| k3(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( ~ m1(C,C,E)
| ~ p2(D,E,D)
| k3(C,C,C) )
| ~ m1(d,d,d)
| ~ p2(d,d,d)
| k3(d,d,d) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
k3(d,d,d),
inference(unit_resolution,[status(thm)],[100,36,97,87]) ).
tff(102,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(d,d,d)
| ~ k3(d,d,d)
| ~ m3(d,d,d)
| q4(d,d) )
<=> ( ~ ! [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(d,d,d)
| ~ k3(d,d,d)
| ~ m3(d,d,d)
| q4(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ( ~ m3(d,d,d)
| ~ q2(d,d,d)
| ~ k3(d,d,d)
| q4(d,d) )
<=> ( ~ q2(d,d,d)
| ~ k3(d,d,d)
| ~ m3(d,d,d)
| q4(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,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(d,d,d)
| ~ q2(d,d,d)
| ~ k3(d,d,d)
| q4(d,d) )
<=> ( ~ ! [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(d,d,d)
| ~ k3(d,d,d)
| ~ m3(d,d,d)
| q4(d,d) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,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(d,d,d)
| ~ q2(d,d,d)
| ~ k3(d,d,d)
| q4(d,d) )
<=> ( ~ ! [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(d,d,d)
| ~ k3(d,d,d)
| ~ m3(d,d,d)
| q4(d,d) ) ),
inference(transitivity,[status(thm)],[104,102]) ).
tff(106,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(d,d,d)
| ~ q2(d,d,d)
| ~ k3(d,d,d)
| q4(d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,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(d,d,d)
| ~ k3(d,d,d)
| ~ m3(d,d,d)
| q4(d,d) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
q4(d,d),
inference(unit_resolution,[status(thm)],[107,101,67,57,43]) ).
tff(109,plain,
^ [D: $i,C: $i] :
refl(( ( n5(C,C)
| ~ q4(D,C) )
<=> ( n5(C,C)
| ~ q4(D,C) ) )),
inference(bind,[status(th)],[]) ).
tff(110,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)],[109]) ).
tff(111,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(112,axiom,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_313) ).
tff(113,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(d,d)
| ~ q4(d,d) )
<=> ( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(d,d)
| ~ q4(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(d,d)
| ~ q4(d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [D: $i,C: $i] :
( n5(C,C)
| ~ q4(D,C) )
| n5(d,d)
| ~ q4(d,d) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
n5(d,d),
inference(unit_resolution,[status(thm)],[118,115,108]) ).
tff(120,plain,
( ~ ! [X: $i] : ~ n5(X,d)
| ~ n5(d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
$false,
inference(unit_resolution,[status(thm)],[120,119,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN157-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.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 12:28:50 EDT 2025
% 0.11/0.33 % 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
%------------------------------------------------------------------------------