TSTP Solution File: SYN705-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN705-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:57:00 EDT 2022
% Result : Unsatisfiable 0.49s 0.58s
% Output : Proof 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 80
% Syntax : Number of formulae : 137 ( 35 unt; 34 typ; 0 def)
% Number of atoms : 475 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 639 ( 296 ~; 291 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 23 >; 23 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 11 con; 0-2 aty)
% Number of variables : 417 ( 377 !; 0 ?; 417 :)
% Comments :
%------------------------------------------------------------------------------
tff(p47_type,type,
p47: ( $i * $i ) > $o ).
tff(c55_type,type,
c55: $i ).
tff(f20_type,type,
f20: ( $i * $i ) > $i ).
tff(c54_type,type,
c54: $i ).
tff(f22_type,type,
f22: ( $i * $i ) > $i ).
tff(c53_type,type,
c53: $i ).
tff(f24_type,type,
f24: ( $i * $i ) > $i ).
tff(c52_type,type,
c52: $i ).
tff(f26_type,type,
f26: ( $i * $i ) > $i ).
tff(c51_type,type,
c51: $i ).
tff(c56_type,type,
c56: $i ).
tff(f5_type,type,
f5: ( $i * $i ) > $i ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(f40_type,type,
f40: ( $i * $i ) > $i ).
tff(f42_type,type,
f42: ( $i * $i ) > $i ).
tff(f44_type,type,
f44: ( $i * $i ) > $i ).
tff(f46_type,type,
f46: ( $i * $i ) > $i ).
tff(c58_type,type,
c58: $i ).
tff(f16_type,type,
f16: ( $i * $i ) > $i ).
tff(f30_type,type,
f30: ( $i * $i ) > $i ).
tff(f32_type,type,
f32: ( $i * $i ) > $i ).
tff(f34_type,type,
f34: ( $i * $i ) > $i ).
tff(f36_type,type,
f36: ( $i * $i ) > $i ).
tff(c57_type,type,
c57: $i ).
tff(f18_type,type,
f18: ( $i * $i ) > $i ).
tff(c50_type,type,
c50: $i ).
tff(c48_type,type,
c48: $i ).
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(c49_type,type,
c49: $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(1,plain,
^ [X38: $i] :
refl(
( p2(X38,X38)
<=> p2(X38,X38) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X38: $i] : p2(X38,X38)
<=> ! [X38: $i] : p2(X38,X38) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X38: $i] : p2(X38,X38)
<=> ! [X38: $i] : p2(X38,X38) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X38: $i] : p2(X38,X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_20) ).
tff(5,plain,
! [X38: $i] : p2(X38,X38),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X38: $i] : p2(X38,X38),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X38: $i] : p2(X38,X38),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X38: $i] : p2(X38,X38)
| p2(c48,c48) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(c48,c48),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X67: $i,X68: $i,X66: $i,X65: $i] :
refl(
( p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68)))
<=> p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68))) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68)))
<=> ! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68))) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68)))
<=> ! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68))) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_80) ).
tff(14,plain,
! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68))),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68))),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68))),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X67: $i,X68: $i,X66: $i,X65: $i] : p3(f8(f10(c49,f13(f16(f18(c50,X65),X66),X67)),X68),f13(f16(f18(c50,f20(f22(f24(f26(c56,X65),X66),X67),X68)),f30(f32(f34(f36(c57,X65),X66),X67),X68)),f40(f42(f44(f46(c58,X65),X66),X67),X68)))
| p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X129: $i,X126: $i,X127: $i,X128: $i] :
refl(
( ( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
<=> ( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
<=> ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
<=> ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X129: $i,X126: $i,X127: $i,X128: $i] :
trans(
monotonicity(
rewrite(
( ( p4(f5(X126,X127),f5(X128,X129))
| ~ p2(X126,X128) )
<=> ( ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ) )),
( ( p4(f5(X126,X127),f5(X128,X129))
| ~ p2(X126,X128)
| ~ p3(X127,X129) )
<=> ( ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129))
| ~ p3(X127,X129) ) )),
rewrite(
( ( ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129))
| ~ p3(X127,X129) )
<=> ( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ) )),
( ( p4(f5(X126,X127),f5(X128,X129))
| ~ p2(X126,X128)
| ~ p3(X127,X129) )
<=> ( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( p4(f5(X126,X127),f5(X128,X129))
| ~ p2(X126,X128)
| ~ p3(X127,X129) )
<=> ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X129: $i,X126: $i,X127: $i,X128: $i] :
( p4(f5(X126,X127),f5(X128,X129))
| ~ p2(X126,X128)
| ~ p3(X127,X129) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_58) ).
tff(25,plain,
! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
| ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p2(c48,c48) )
<=> ( ~ ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
| ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p2(c48,c48) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| ~ p2(c48,c48)
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) )
<=> ( ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p2(c48,c48) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
| ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| ~ p2(c48,c48)
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) )
<=> ( ~ ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
| ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p2(c48,c48) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
| ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| ~ p2(c48,c48)
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) )
<=> ( ~ ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
| ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p2(c48,c48) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
| ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| ~ p2(c48,c48)
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X129: $i,X126: $i,X127: $i,X128: $i] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) )
| ~ p3(f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54),f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))
| p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p2(c48,c48) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
^ [X162: $i] :
refl(
( p7(X162,X162)
<=> p7(X162,X162) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X162: $i] : p7(X162,X162)
<=> ! [X162: $i] : p7(X162,X162) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X162: $i] : p7(X162,X162)
<=> ! [X162: $i] : p7(X162,X162) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [X162: $i] : p7(X162,X162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_3) ).
tff(40,plain,
! [X162: $i] : p7(X162,X162),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X162: $i] : p7(X162,X162),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X162: $i] : p7(X162,X162),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [X162: $i] : p7(X162,X162)
| p7(c55,c55) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
p7(c55,c55),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
<=> p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_77) ).
tff(47,plain,
p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
^ [X152: $i,X154: $i,X151: $i,X153: $i] :
refl(
( ( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
<=> ( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
<=> ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
<=> ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [X152: $i,X154: $i,X151: $i,X153: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p47(X151,X152)
| ~ p47(X153,X154) )
<=> ( ~ p47(X153,X154)
| p47(X151,X152) ) )),
( ( p47(X151,X152)
| ~ p47(X153,X154)
| ~ p7(X154,X152) )
<=> ( ~ p47(X153,X154)
| p47(X151,X152)
| ~ p7(X154,X152) ) )),
rewrite(
( ( ~ p47(X153,X154)
| p47(X151,X152)
| ~ p7(X154,X152) )
<=> ( ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ) )),
( ( p47(X151,X152)
| ~ p47(X153,X154)
| ~ p7(X154,X152) )
<=> ( ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ) )),
( ( p47(X151,X152)
| ~ p47(X153,X154)
| ~ p7(X154,X152)
| ~ p4(X153,X151) )
<=> ( ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152)
| ~ p4(X153,X151) ) )),
rewrite(
( ( ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152)
| ~ p4(X153,X151) )
<=> ( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ) )),
( ( p47(X151,X152)
| ~ p47(X153,X154)
| ~ p7(X154,X152)
| ~ p4(X153,X151) )
<=> ( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( p47(X151,X152)
| ~ p47(X153,X154)
| ~ p7(X154,X152)
| ~ p4(X153,X151) )
<=> ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [X152: $i,X154: $i,X151: $i,X153: $i] :
( p47(X151,X152)
| ~ p47(X153,X154)
| ~ p7(X154,X152)
| ~ p4(X153,X151) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_53) ).
tff(54,plain,
! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| ~ p7(c55,c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55)
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) )
<=> ( ~ ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| ~ p7(c55,c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55)
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p7(c55,c55)
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55) )
<=> ( ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| ~ p7(c55,c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55)
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p7(c55,c55)
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55) )
<=> ( ~ ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| ~ p7(c55,c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55)
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p7(c55,c55)
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55) )
<=> ( ~ ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| ~ p7(c55,c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55)
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))))
| ~ p7(c55,c55)
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [X152: $i,X154: $i,X151: $i,X153: $i] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) )
| ~ p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55)
| ~ p7(c55,c55)
| p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55)
| ~ p4(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54)))) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55),
inference(unit_resolution,[status(thm)],[63,57,47,44,35]) ).
tff(65,plain,
^ [X148: $i,X150: $i,X147: $i,X149: $i] :
refl(
( ( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) )
<=> ( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) )
<=> ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) )
<=> ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_74) ).
tff(69,plain,
! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ( ~ ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) )
| p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55)
| ~ p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55) )
<=> ( ~ ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) )
| p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55)
| ~ p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ~ ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) )
| p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55)
| ~ p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(X147,X148)
| ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) )
| p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55)
| ~ p47(f5(c48,f13(f16(f18(c50,f20(f22(f24(f26(c56,c51),c52),c53),c54)),f30(f32(f34(f36(c57,c51),c52),c53),c54)),f40(f42(f44(f46(c58,c51),c52),c53),c54))),c55) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55),
inference(unit_resolution,[status(thm)],[74,71,64]) ).
tff(76,plain,
^ [X148: $i,X150: $i,X147: $i,X149: $i] :
refl(
( ( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) )
<=> ( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) )
<=> ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) )
<=> ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_76) ).
tff(80,plain,
! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55)
<=> ~ p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
~ p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p47_51) ).
tff(85,plain,
~ p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ( ~ ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) )
| p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55)
| ~ p47(c51,c55) )
<=> ( ~ ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) )
| p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55)
| ~ p47(c51,c55) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) )
| p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55)
| ~ p47(c51,c55) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [X148: $i,X150: $i,X147: $i,X149: $i] :
( p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| ~ p47(X147,X148) )
| p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55)
| ~ p47(c51,c55) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
~ p47(c51,c55),
inference(unit_resolution,[status(thm)],[88,85,82]) ).
tff(90,plain,
^ [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
refl(
( ( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) )
<=> ( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) )
<=> ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
( ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) )
<=> ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
^ [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
rewrite(
( ( p47(X65,X69)
| ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69) )
<=> ( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( p47(X65,X69)
| ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69) )
<=> ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,axiom,
! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( p47(X65,X69)
| ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_75) ).
tff(96,plain,
! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
( ( ~ ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) )
| ~ p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55)
| p47(c51,c55) )
<=> ( ~ ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) )
| ~ p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55)
| p47(c51,c55) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) )
| ~ p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55)
| p47(c51,c55) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( ~ ! [X67: $i,X68: $i,X66: $i,X65: $i,X69: $i] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) )
| ~ p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55)
| p47(c51,c55) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
$false,
inference(unit_resolution,[status(thm)],[102,99,89,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : SYN705-1 : TPTP v8.1.0. Released v2.5.0.
% 0.14/0.16 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.17/0.38 % Computer : n017.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon Sep 5 06:03:55 EDT 2022
% 0.17/0.38 % CPUTime :
% 0.17/0.38 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.17/0.38 Usage: tptp [options] [-file:]file
% 0.17/0.38 -h, -? prints this message.
% 0.17/0.38 -smt2 print SMT-LIB2 benchmark.
% 0.17/0.38 -m, -model generate model.
% 0.17/0.38 -p, -proof generate proof.
% 0.17/0.38 -c, -core generate unsat core of named formulas.
% 0.17/0.38 -st, -statistics display statistics.
% 0.17/0.38 -t:timeout set timeout (in second).
% 0.17/0.38 -smt2status display status in smt2 format instead of SZS.
% 0.17/0.38 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.17/0.38 -<param>:<value> configuration parameter and value.
% 0.17/0.38 -o:<output-file> file to place output in.
% 0.49/0.58 % SZS status Unsatisfiable
% 0.49/0.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------