%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO038-1.003.003 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:41:12 AM UTC 2025
% Result : Unsatisfiable 126.45s 126.75s
% Output : Proof 126.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 63
% Syntax : Number of formulae : 207 ( 105 unt; 0 typ; 0 def)
% Number of atoms : 479 ( 121 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 498 ( 231 ~; 224 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 130 ( 124 !; 0 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
tff(d_type,type,
d: $i > $o ).
tff(s_type,type,
s: $i > $i ).
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(one_type,type,
one: $i ).
tff(1,plain,
^ [N: $i,X: $i] :
refl(( ( f(s(N),s(X)) = f(N,f(s(N),X)) )
<=> ( f(s(N),s(X)) = f(N,f(s(N),X)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
<=> ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
<=> ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(5,plain,
! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(s(one)),s(s(one))) = f(s(one),f(s(s(one)),s(one))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
f(s(s(one)),s(s(one))) = f(s(one),f(s(s(one)),s(one))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
f(s(one),f(s(s(one)),s(one))) = f(s(s(one)),s(s(one))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [N: $i] :
refl(( ( f(N,one) = s(one) )
<=> ( f(N,one) = s(one) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [N: $i] : ( f(N,one) = s(one) )
<=> ! [N: $i] : ( f(N,one) = s(one) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [N: $i] : ( f(N,one) = s(one) )
<=> ! [N: $i] : ( f(N,one) = s(one) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [N: $i] : ( f(N,one) = s(one) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(15,plain,
! [N: $i] : ( f(N,one) = s(one) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [N: $i] : ( f(N,one) = s(one) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [N: $i] : ( f(N,one) = s(one) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [N: $i] : ( f(N,one) = s(one) )
| ( f(one,one) = s(one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
f(one,one) = s(one),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
s(f(one,one)) = s(s(one)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
s(s(one)) = s(f(one,one)),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
s(s(s(one))) = s(s(f(one,one))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
s(s(f(one,one))) = s(s(s(one))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
^ [X: $i] :
refl(( ( f(one,s(X)) = s(s(f(one,X))) )
<=> ( f(one,s(X)) = s(s(f(one,X))) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
<=> ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
<=> ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(28,plain,
! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(one)) = s(s(f(one,one))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
f(one,s(one)) = s(s(f(one,one))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ! [N: $i] : ( f(N,one) = s(one) )
| ( f(s(one),one) = s(one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
f(s(one),one) = s(one),
inference(unit_resolution,[status(thm)],[33,17]) ).
tff(35,plain,
f(one,f(s(one),one)) = f(one,s(one)),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(one),s(one)) = f(one,f(s(one),one)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
f(s(one),s(one)) = f(one,f(s(one),one)),
inference(unit_resolution,[status(thm)],[36,7]) ).
tff(38,plain,
( ~ ! [N: $i] : ( f(N,one) = s(one) )
| ( f(s(s(one)),one) = s(one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
f(s(s(one)),one) = s(one),
inference(unit_resolution,[status(thm)],[38,17]) ).
tff(40,plain,
f(s(one),f(s(s(one)),one)) = f(s(one),s(one)),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(s(one)),s(one)) = f(s(one),f(s(s(one)),one)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
f(s(s(one)),s(one)) = f(s(one),f(s(s(one)),one)),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
f(s(s(one)),s(one)) = s(s(s(one))),
inference(transitivity,[status(thm)],[42,40,37,35,32,23]) ).
tff(44,plain,
f(s(one),f(s(s(one)),s(one))) = f(s(one),s(s(s(one)))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
f(s(one),s(s(s(one)))) = f(s(one),f(s(s(one)),s(one))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(one),s(s(s(one)))) = f(one,f(s(one),s(s(one)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
f(s(one),s(s(s(one)))) = f(one,f(s(one),s(s(one)))),
inference(unit_resolution,[status(thm)],[46,7]) ).
tff(48,plain,
f(one,f(s(one),s(s(one)))) = f(s(one),s(s(s(one)))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(one),s(s(one))) = f(one,f(s(one),s(one))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
f(s(one),s(s(one))) = f(one,f(s(one),s(one))),
inference(unit_resolution,[status(thm)],[49,7]) ).
tff(51,plain,
f(one,f(s(one),s(one))) = f(s(one),s(s(one))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
f(s(one),s(one)) = s(s(f(one,one))),
inference(transitivity,[status(thm)],[37,35,32]) ).
tff(53,plain,
f(one,f(s(one),s(one))) = f(one,s(s(f(one,one)))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
f(one,s(s(f(one,one)))) = f(one,f(s(one),s(one))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(f(one,one)))) = s(s(f(one,s(f(one,one))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
f(one,s(s(f(one,one)))) = s(s(f(one,s(f(one,one))))),
inference(unit_resolution,[status(thm)],[55,30]) ).
tff(57,plain,
s(s(f(one,s(f(one,one))))) = f(one,s(s(f(one,one)))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
s(s(f(one,s(f(one,one))))) = f(s(one),s(s(one))),
inference(transitivity,[status(thm)],[57,54,51]) ).
tff(59,plain,
f(one,s(s(f(one,s(f(one,one)))))) = f(one,f(s(one),s(s(one)))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
f(one,s(s(s(one)))) = f(one,s(s(f(one,one)))),
inference(monotonicity,[status(thm)],[22]) ).
tff(61,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(s(one)))) = s(s(f(one,s(s(one))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
f(one,s(s(s(one)))) = s(s(f(one,s(s(one))))),
inference(unit_resolution,[status(thm)],[61,30]) ).
tff(63,plain,
s(s(f(one,s(s(one))))) = f(one,s(s(s(one)))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
s(s(f(one,s(s(one))))) = s(s(f(one,s(f(one,one))))),
inference(transitivity,[status(thm)],[63,60,56]) ).
tff(65,plain,
f(one,s(s(f(one,s(s(one)))))) = f(one,s(s(f(one,s(f(one,one)))))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(f(one,s(s(one)))))) = s(s(f(one,s(f(one,s(s(one))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
f(one,s(s(f(one,s(s(one)))))) = s(s(f(one,s(f(one,s(s(one))))))),
inference(unit_resolution,[status(thm)],[66,30]) ).
tff(68,plain,
s(s(f(one,s(f(one,s(s(one))))))) = f(one,s(s(f(one,s(s(one)))))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
s(s(f(one,s(f(one,s(s(one))))))) = f(s(s(one)),s(s(one))),
inference(transitivity,[status(thm)],[68,65,59,48,45,10]) ).
tff(70,plain,
( d(s(s(f(one,s(f(one,s(s(one))))))))
<=> d(f(s(s(one)),s(s(one)))) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( d(f(s(s(one)),s(s(one))))
<=> d(s(s(f(one,s(f(one,s(s(one)))))))) ),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ d(f(s(s(one)),s(s(one))))
<=> ~ d(s(s(f(one,s(f(one,s(s(one)))))))) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ~ d(f(s(s(one)),s(s(one))))
<=> ~ d(f(s(s(one)),s(s(one)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
~ d(f(s(s(one)),s(s(one)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(75,plain,
~ d(f(s(s(one)),s(s(one)))),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
~ d(s(s(f(one,s(f(one,s(s(one)))))))),
inference(modus_ponens,[status(thm)],[75,72]) ).
tff(77,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(one))) = s(s(f(one,s(one)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
f(one,s(s(one))) = s(s(f(one,s(one)))),
inference(unit_resolution,[status(thm)],[77,30]) ).
tff(79,plain,
s(s(f(one,s(one)))) = f(one,s(s(one))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
s(s(s(f(one,s(one))))) = s(f(one,s(s(one)))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
s(f(one,s(s(one)))) = s(s(s(f(one,s(one))))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
f(one,s(f(one,s(s(one))))) = f(one,s(s(s(f(one,s(one)))))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
f(one,s(s(s(f(one,s(one)))))) = f(one,s(f(one,s(s(one))))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(s(f(one,s(one)))))) = s(s(f(one,s(s(f(one,s(one))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
f(one,s(s(s(f(one,s(one)))))) = s(s(f(one,s(s(f(one,s(one))))))),
inference(unit_resolution,[status(thm)],[84,30]) ).
tff(86,plain,
s(s(f(one,s(s(f(one,s(one))))))) = f(one,s(s(s(f(one,s(one)))))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
s(s(f(one,s(s(f(one,s(one))))))) = f(one,s(f(one,s(s(one))))),
inference(transitivity,[status(thm)],[86,83]) ).
tff(88,plain,
s(s(s(f(one,s(s(f(one,s(one)))))))) = s(f(one,s(f(one,s(s(one)))))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( d(s(s(s(f(one,s(s(f(one,s(one)))))))))
<=> d(s(f(one,s(f(one,s(s(one))))))) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(f(one,s(one))))) = s(s(f(one,s(f(one,s(one)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
f(one,s(s(f(one,s(one))))) = s(s(f(one,s(f(one,s(one)))))),
inference(unit_resolution,[status(thm)],[90,30]) ).
tff(92,plain,
s(s(f(one,s(f(one,s(one)))))) = f(one,s(s(f(one,s(one))))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
s(s(s(f(one,s(f(one,s(one))))))) = s(f(one,s(s(f(one,s(one)))))),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( d(s(s(s(f(one,s(f(one,s(one))))))))
<=> d(s(f(one,s(s(f(one,s(one))))))) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
s(s(f(one,one))) = f(one,s(one)),
inference(symmetry,[status(thm)],[32]) ).
tff(96,plain,
s(s(s(f(one,one)))) = s(f(one,s(one))),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
s(f(one,s(one))) = s(s(s(f(one,one)))),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
f(one,s(f(one,s(one)))) = f(one,s(s(s(f(one,one))))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
f(one,s(s(s(f(one,one))))) = f(one,s(f(one,s(one)))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(s(f(one,one))))) = s(s(f(one,s(s(f(one,one)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
f(one,s(s(s(f(one,one))))) = s(s(f(one,s(s(f(one,one)))))),
inference(unit_resolution,[status(thm)],[100,30]) ).
tff(102,plain,
s(s(f(one,s(s(f(one,one)))))) = f(one,s(s(s(f(one,one))))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
s(s(f(one,s(s(f(one,one)))))) = f(one,s(f(one,s(one)))),
inference(transitivity,[status(thm)],[102,99]) ).
tff(104,plain,
s(s(s(f(one,s(s(f(one,one))))))) = s(f(one,s(f(one,s(one))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( d(s(s(s(f(one,s(s(f(one,one))))))))
<=> d(s(f(one,s(f(one,s(one)))))) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
s(s(s(f(one,s(f(one,one)))))) = s(f(one,s(s(f(one,one))))),
inference(monotonicity,[status(thm)],[57]) ).
tff(107,plain,
( d(s(s(s(f(one,s(f(one,one)))))))
<=> d(s(f(one,s(s(f(one,one)))))) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( d(s(s(f(one,s(s(one))))))
<=> d(s(s(f(one,s(f(one,one)))))) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(109,plain,
( d(s(s(s(f(one,s(one))))))
<=> d(s(f(one,s(s(one))))) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(110,plain,
( d(s(s(s(f(one,one)))))
<=> d(s(f(one,s(one)))) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(111,plain,
( d(s(f(one,one)))
<=> d(s(s(one))) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(112,plain,
( d(s(s(one)))
<=> d(s(f(one,one))) ),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
^ [X: $i] :
refl(( ( d(s(X))
| ~ d(X) )
<=> ( d(s(X))
| ~ d(X) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [X: $i] :
( d(s(X))
| ~ d(X) )
<=> ! [X: $i] :
( d(s(X))
| ~ d(X) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [X: $i] :
( d(s(X))
| ~ d(X) )
<=> ! [X: $i] :
( d(s(X))
| ~ d(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
^ [X: $i] :
rewrite(( ( ~ d(X)
| d(s(X)) )
<=> ( d(s(X))
| ~ d(X) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [X: $i] :
( ~ d(X)
| d(s(X)) )
<=> ! [X: $i] :
( d(s(X))
| ~ d(X) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [X: $i] :
( ~ d(X)
| d(s(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(119,plain,
! [X: $i] :
( d(s(X))
| ~ d(X) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [X: $i] :
( d(s(X))
| ~ d(X) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [X: $i] :
( d(s(X))
| ~ d(X) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [X: $i] :
( d(s(X))
| ~ d(X) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( d(one)
<=> d(one) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,axiom,
d(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(125,plain,
d(one),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(one))
| ~ d(one) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(one))
| ~ d(one) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(one))
| ~ d(one) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(one))
| ~ d(one) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
d(s(one)),
inference(unit_resolution,[status(thm)],[128,125,122]) ).
tff(130,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(one)))
| ~ d(s(one)) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(one)))
| ~ d(s(one)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(one)))
| ~ d(s(one)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(one)))
| ~ d(s(one)) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
d(s(s(one))),
inference(unit_resolution,[status(thm)],[132,122,129]) ).
tff(134,plain,
d(s(f(one,one))),
inference(modus_ponens,[status(thm)],[133,112]) ).
tff(135,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,one))))
| ~ d(s(f(one,one))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,one))))
| ~ d(s(f(one,one))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,one))))
| ~ d(s(f(one,one))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,one))))
| ~ d(s(f(one,one))) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( d(s(s(f(one,one))))
| ~ d(s(f(one,one))) ),
inference(unit_resolution,[status(thm)],[137,122]) ).
tff(139,plain,
d(s(s(f(one,one)))),
inference(unit_resolution,[status(thm)],[138,134]) ).
tff(140,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,one)))))
| ~ d(s(s(f(one,one)))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,one)))))
| ~ d(s(s(f(one,one)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,one)))))
| ~ d(s(s(f(one,one)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,one)))))
| ~ d(s(s(f(one,one)))) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
( d(s(s(s(f(one,one)))))
| ~ d(s(s(f(one,one)))) ),
inference(unit_resolution,[status(thm)],[142,122]) ).
tff(144,plain,
d(s(s(s(f(one,one))))),
inference(unit_resolution,[status(thm)],[143,139]) ).
tff(145,plain,
d(s(f(one,s(one)))),
inference(modus_ponens,[status(thm)],[144,110]) ).
tff(146,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
( d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) ),
inference(unit_resolution,[status(thm)],[148,122]) ).
tff(150,plain,
d(s(s(f(one,s(one))))),
inference(unit_resolution,[status(thm)],[149,145]) ).
tff(151,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(one))))))
| ~ d(s(s(f(one,s(one))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(one))))))
| ~ d(s(s(f(one,s(one))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(one))))))
| ~ d(s(s(f(one,s(one))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(one))))))
| ~ d(s(s(f(one,s(one))))) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( d(s(s(s(f(one,s(one))))))
| ~ d(s(s(f(one,s(one))))) ),
inference(unit_resolution,[status(thm)],[153,122]) ).
tff(155,plain,
d(s(s(s(f(one,s(one)))))),
inference(unit_resolution,[status(thm)],[154,150]) ).
tff(156,plain,
d(s(f(one,s(s(one))))),
inference(modus_ponens,[status(thm)],[155,109]) ).
tff(157,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
( d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) ),
inference(unit_resolution,[status(thm)],[159,122]) ).
tff(161,plain,
d(s(s(f(one,s(s(one)))))),
inference(unit_resolution,[status(thm)],[160,156]) ).
tff(162,plain,
d(s(s(f(one,s(f(one,one)))))),
inference(modus_ponens,[status(thm)],[161,108]) ).
tff(163,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(f(one,one)))))))
| ~ d(s(s(f(one,s(f(one,one)))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(f(one,one)))))))
| ~ d(s(s(f(one,s(f(one,one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(f(one,one)))))))
| ~ d(s(s(f(one,s(f(one,one)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(f(one,one)))))))
| ~ d(s(s(f(one,s(f(one,one)))))) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
( d(s(s(s(f(one,s(f(one,one)))))))
| ~ d(s(s(f(one,s(f(one,one)))))) ),
inference(unit_resolution,[status(thm)],[165,122]) ).
tff(167,plain,
d(s(s(s(f(one,s(f(one,one))))))),
inference(unit_resolution,[status(thm)],[166,162]) ).
tff(168,plain,
d(s(f(one,s(s(f(one,one)))))),
inference(modus_ponens,[status(thm)],[167,107]) ).
tff(169,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,one)))))))
| ~ d(s(f(one,s(s(f(one,one)))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,one)))))))
| ~ d(s(f(one,s(s(f(one,one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,one)))))))
| ~ d(s(f(one,s(s(f(one,one)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,one)))))))
| ~ d(s(f(one,s(s(f(one,one)))))) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
( d(s(s(f(one,s(s(f(one,one)))))))
| ~ d(s(f(one,s(s(f(one,one)))))) ),
inference(unit_resolution,[status(thm)],[171,122]) ).
tff(173,plain,
d(s(s(f(one,s(s(f(one,one))))))),
inference(unit_resolution,[status(thm)],[172,168]) ).
tff(174,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(s(f(one,one))))))))
| ~ d(s(s(f(one,s(s(f(one,one))))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(s(f(one,one))))))))
| ~ d(s(s(f(one,s(s(f(one,one))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(s(f(one,one))))))))
| ~ d(s(s(f(one,s(s(f(one,one))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(s(f(one,one))))))))
| ~ d(s(s(f(one,s(s(f(one,one))))))) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
( d(s(s(s(f(one,s(s(f(one,one))))))))
| ~ d(s(s(f(one,s(s(f(one,one))))))) ),
inference(unit_resolution,[status(thm)],[176,122]) ).
tff(178,plain,
d(s(s(s(f(one,s(s(f(one,one)))))))),
inference(unit_resolution,[status(thm)],[177,173]) ).
tff(179,plain,
d(s(f(one,s(f(one,s(one)))))),
inference(modus_ponens,[status(thm)],[178,105]) ).
tff(180,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
( d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) ),
inference(unit_resolution,[status(thm)],[182,122]) ).
tff(184,plain,
d(s(s(f(one,s(f(one,s(one))))))),
inference(unit_resolution,[status(thm)],[183,179]) ).
tff(185,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(f(one,s(one))))))))
| ~ d(s(s(f(one,s(f(one,s(one))))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(f(one,s(one))))))))
| ~ d(s(s(f(one,s(f(one,s(one))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(f(one,s(one))))))))
| ~ d(s(s(f(one,s(f(one,s(one))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(f(one,s(one))))))))
| ~ d(s(s(f(one,s(f(one,s(one))))))) ),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
( d(s(s(s(f(one,s(f(one,s(one))))))))
| ~ d(s(s(f(one,s(f(one,s(one))))))) ),
inference(unit_resolution,[status(thm)],[187,122]) ).
tff(189,plain,
d(s(s(s(f(one,s(f(one,s(one)))))))),
inference(unit_resolution,[status(thm)],[188,184]) ).
tff(190,plain,
d(s(f(one,s(s(f(one,s(one))))))),
inference(modus_ponens,[status(thm)],[189,94]) ).
tff(191,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
( d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) ),
inference(unit_resolution,[status(thm)],[193,122]) ).
tff(195,plain,
d(s(s(f(one,s(s(f(one,s(one)))))))),
inference(unit_resolution,[status(thm)],[194,190]) ).
tff(196,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(s(f(one,s(one)))))))))
| ~ d(s(s(f(one,s(s(f(one,s(one)))))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(s(f(one,s(one)))))))))
| ~ d(s(s(f(one,s(s(f(one,s(one)))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(s(f(one,s(one)))))))))
| ~ d(s(s(f(one,s(s(f(one,s(one)))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(s(f(one,s(s(f(one,s(one)))))))))
| ~ d(s(s(f(one,s(s(f(one,s(one)))))))) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
( d(s(s(s(f(one,s(s(f(one,s(one)))))))))
| ~ d(s(s(f(one,s(s(f(one,s(one)))))))) ),
inference(unit_resolution,[status(thm)],[198,122]) ).
tff(200,plain,
d(s(s(s(f(one,s(s(f(one,s(one))))))))),
inference(unit_resolution,[status(thm)],[199,195]) ).
tff(201,plain,
d(s(f(one,s(f(one,s(s(one))))))),
inference(modus_ponens,[status(thm)],[200,89]) ).
tff(202,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(203,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
( d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) ),
inference(unit_resolution,[status(thm)],[204,122]) ).
tff(206,plain,
d(s(s(f(one,s(f(one,s(s(one)))))))),
inference(unit_resolution,[status(thm)],[205,201]) ).
tff(207,plain,
$false,
inference(unit_resolution,[status(thm)],[206,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO038-1.003.003 : TPTP v9.0.0. Released v5.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:04:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 126.45/126.75 % SZS status Unsatisfiable
% 126.45/126.75 % SZS output start Proof
% See solution above
% 126.84/127.13 % E exiting
%------------------------------------------------------------------------------