TSTP Solution File: SYN311-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN311-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Thu Sep 29 23:54:38 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 57
% Syntax : Number of formulae : 113 ( 27 unt; 7 typ; 0 def)
% Number of atoms : 391 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 532 ( 255 ~; 240 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 448 ( 416 !; 0 ?; 448 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: ( $i * $i * $i * $i ) > $o ).
tff(g_type,type,
g: $i > $i ).
tff(c_type,type,
c: $i ).
tff(d_type,type,
d: $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(f_type,type,
f: $i > $i ).
tff(1,plain,
( ~ p(f(g(d)),f(g(c)),f(g(b)),f(g(a)))
<=> ~ p(f(g(d)),f(g(c)),f(g(b)),f(g(a))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ p(f(g(d)),f(g(c)),f(g(b)),f(g(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
tff(3,plain,
~ p(f(g(d)),f(g(c)),f(g(b)),f(g(a))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
refl(
( ( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
<=> ( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
rewrite(
( ( p(f(X),X1,X2,X3)
| ~ p(X,X1,X2,X3) )
<=> ( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(f(X),X1,X2,X3)
| ~ p(X,X1,X2,X3) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(f(X),X1,X2,X3)
| ~ p(X,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
tff(10,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(d),f(g(c)),f(g(b)),f(g(a)))
| p(f(g(d)),f(g(c)),f(g(b)),f(g(a))) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(d),f(g(c)),f(g(b)),f(g(a)))
| p(f(g(d)),f(g(c)),f(g(b)),f(g(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(d),f(g(c)),f(g(b)),f(g(a)))
| p(f(g(d)),f(g(c)),f(g(b)),f(g(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(d),f(g(c)),f(g(b)),f(g(a)))
| p(f(g(d)),f(g(c)),f(g(b)),f(g(a))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ p(g(d),f(g(c)),f(g(b)),f(g(a))),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
refl(
( ( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
<=> ( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
rewrite(
( ( p(X3,X2,X1,X)
| ~ p(X,X1,X2,X3) )
<=> ( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(X3,X2,X1,X)
| ~ p(X,X1,X2,X3) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(X3,X2,X1,X)
| ~ p(X,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
tff(24,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(f(g(a)),f(g(b)),f(g(c)),g(d))
| p(g(d),f(g(c)),f(g(b)),f(g(a))) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(f(g(a)),f(g(b)),f(g(c)),g(d))
| p(g(d),f(g(c)),f(g(b)),f(g(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(f(g(a)),f(g(b)),f(g(c)),g(d))
| p(g(d),f(g(c)),f(g(b)),f(g(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(f(g(a)),f(g(b)),f(g(c)),g(d))
| p(g(d),f(g(c)),f(g(b)),f(g(a))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
~ p(f(g(a)),f(g(b)),f(g(c)),g(d)),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(a),f(g(b)),f(g(c)),g(d))
| p(f(g(a)),f(g(b)),f(g(c)),g(d)) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(a),f(g(b)),f(g(c)),g(d))
| p(f(g(a)),f(g(b)),f(g(c)),g(d)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(a),f(g(b)),f(g(c)),g(d))
| p(f(g(a)),f(g(b)),f(g(c)),g(d)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(a),f(g(b)),f(g(c)),g(d))
| p(f(g(a)),f(g(b)),f(g(c)),g(d)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ p(g(a),f(g(b)),f(g(c)),g(d)),
inference(unit_resolution,[status(thm)],[34,13,31]) ).
tff(36,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
refl(
( ( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
<=> ( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
rewrite(
( ( p(X,X1,X2,g(X3))
| ~ p(X,X1,X2,X3) )
<=> ( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(X,X1,X2,g(X3))
| ~ p(X,X1,X2,X3) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(X,X1,X2,g(X3))
| ~ p(X,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
tff(42,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(a),f(g(b)),f(g(c)),d)
| p(g(a),f(g(b)),f(g(c)),g(d)) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(a),f(g(b)),f(g(c)),d)
| p(g(a),f(g(b)),f(g(c)),g(d)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(a),f(g(b)),f(g(c)),d)
| p(g(a),f(g(b)),f(g(c)),g(d)) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(a),f(g(b)),f(g(c)),d)
| p(g(a),f(g(b)),f(g(c)),g(d)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ p(g(a),f(g(b)),f(g(c)),d),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
refl(
( ( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
<=> ( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
rewrite(
( ( p(X3,X,X1,X2)
| ~ p(X,X1,X2,X3) )
<=> ( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(X3,X,X1,X2)
| ~ p(X,X1,X2,X3) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(X3,X,X1,X2)
| ~ p(X,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
tff(56,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(f(g(b)),f(g(c)),d,g(a))
| p(g(a),f(g(b)),f(g(c)),d) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(f(g(b)),f(g(c)),d,g(a))
| p(g(a),f(g(b)),f(g(c)),d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(f(g(b)),f(g(c)),d,g(a))
| p(g(a),f(g(b)),f(g(c)),d) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(f(g(b)),f(g(c)),d,g(a))
| p(g(a),f(g(b)),f(g(c)),d) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ p(f(g(b)),f(g(c)),d,g(a)),
inference(unit_resolution,[status(thm)],[62,59,49]) ).
tff(64,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(b),f(g(c)),d,g(a))
| p(f(g(b)),f(g(c)),d,g(a)) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(b),f(g(c)),d,g(a))
| p(f(g(b)),f(g(c)),d,g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(b),f(g(c)),d,g(a))
| p(f(g(b)),f(g(c)),d,g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(b),f(g(c)),d,g(a))
| p(f(g(b)),f(g(c)),d,g(a)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
~ p(g(b),f(g(c)),d,g(a)),
inference(unit_resolution,[status(thm)],[66,13,63]) ).
tff(68,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(b),f(g(c)),d,a)
| p(g(b),f(g(c)),d,g(a)) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(b),f(g(c)),d,a)
| p(g(b),f(g(c)),d,g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(b),f(g(c)),d,a)
| p(g(b),f(g(c)),d,g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(b),f(g(c)),d,a)
| p(g(b),f(g(c)),d,g(a)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ p(g(b),f(g(c)),d,a),
inference(unit_resolution,[status(thm)],[70,45,67]) ).
tff(72,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(f(g(c)),d,a,g(b))
| p(g(b),f(g(c)),d,a) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(f(g(c)),d,a,g(b))
| p(g(b),f(g(c)),d,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(f(g(c)),d,a,g(b))
| p(g(b),f(g(c)),d,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(f(g(c)),d,a,g(b))
| p(g(b),f(g(c)),d,a) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ p(f(g(c)),d,a,g(b)),
inference(unit_resolution,[status(thm)],[74,59,71]) ).
tff(76,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(c),d,a,g(b))
| p(f(g(c)),d,a,g(b)) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(c),d,a,g(b))
| p(f(g(c)),d,a,g(b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(c),d,a,g(b))
| p(f(g(c)),d,a,g(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(f(X),X1,X2,X3) )
| ~ p(g(c),d,a,g(b))
| p(f(g(c)),d,a,g(b)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
~ p(g(c),d,a,g(b)),
inference(unit_resolution,[status(thm)],[78,13,75]) ).
tff(80,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(c),d,a,b)
| p(g(c),d,a,g(b)) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(c),d,a,b)
| p(g(c),d,a,g(b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(c),d,a,b)
| p(g(c),d,a,g(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(g(c),d,a,b)
| p(g(c),d,a,g(b)) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ p(g(c),d,a,b),
inference(unit_resolution,[status(thm)],[82,45,79]) ).
tff(84,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(b,a,d,g(c))
| p(g(c),d,a,b) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(b,a,d,g(c))
| p(g(c),d,a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(b,a,d,g(c))
| p(g(c),d,a,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(b,a,d,g(c))
| p(g(c),d,a,b) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
~ p(b,a,d,g(c)),
inference(unit_resolution,[status(thm)],[86,27,83]) ).
tff(88,plain,
( p(a,b,c,d)
<=> p(a,b,c,d) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
p(a,b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
tff(90,plain,
p(a,b,c,d),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(a,b,c,d)
| p(d,c,b,a) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(a,b,c,d)
| p(d,c,b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(a,b,c,d)
| p(d,c,b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X2,X1,X) )
| ~ p(a,b,c,d)
| p(d,c,b,a) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
p(d,c,b,a),
inference(unit_resolution,[status(thm)],[93,27,90]) ).
tff(95,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(d,c,b,a)
| p(a,d,c,b) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(d,c,b,a)
| p(a,d,c,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(d,c,b,a)
| p(a,d,c,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(d,c,b,a)
| p(a,d,c,b) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
p(a,d,c,b),
inference(unit_resolution,[status(thm)],[97,59,94]) ).
tff(99,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(a,d,c,b)
| p(b,a,d,c) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(a,d,c,b)
| p(b,a,d,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(a,d,c,b)
| p(b,a,d,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X3,X,X1,X2) )
| ~ p(a,d,c,b)
| p(b,a,d,c) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
p(b,a,d,c),
inference(unit_resolution,[status(thm)],[101,59,98]) ).
tff(103,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(b,a,d,c)
| p(b,a,d,g(c)) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(b,a,d,c)
| p(b,a,d,g(c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(b,a,d,c)
| p(b,a,d,g(c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2,X3)
| p(X,X1,X2,g(X3)) )
| ~ p(b,a,d,c)
| p(b,a,d,g(c)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
$false,
inference(unit_resolution,[status(thm)],[105,45,102,87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN311-1 : TPTP v8.1.0. Released v1.2.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:36:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------