TSTP Solution File: SYN713-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN713-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 23:57:02 EDT 2022
% Result : Unsatisfiable 0.47s 0.54s
% Output : Proof 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 95
% Syntax : Number of formulae : 164 ( 44 unt; 38 typ; 0 def)
% Number of atoms : 579 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 741 ( 327 ~; 350 |; 0 &)
% ( 64 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 39 ( 39 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 23 >; 23 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 15 con; 0-2 aty)
% Number of variables : 378 ( 335 !; 0 ?; 378 :)
% Comments :
%------------------------------------------------------------------------------
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(f14_type,type,
f14: ( $i * $i ) > $i ).
tff(f23_type,type,
f23: ( $i * $i ) > $i ).
tff(c77_type,type,
c77: $i ).
tff(c74_type,type,
c74: $i ).
tff(f17_type,type,
f17: ( $i * $i ) > $i ).
tff(c67_type,type,
c67: $i ).
tff(c66_type,type,
c66: $i ).
tff(c65_type,type,
c65: $i ).
tff(c68_type,type,
c68: $i ).
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(p12_type,type,
p12: ( $i * $i ) > $o ).
tff(p13_type,type,
p13: ( $i * $i ) > $o ).
tff(p58_type,type,
p58: ( $i * $i ) > $o ).
tff(f19_type,type,
f19: ( $i * $i ) > $i ).
tff(f22_type,type,
f22: ( $i * $i ) > $i ).
tff(c69_type,type,
c69: $i ).
tff(c70_type,type,
c70: $i ).
tff(f31_type,type,
f31: ( $i * $i ) > $i ).
tff(f33_type,type,
f33: ( $i * $i ) > $i ).
tff(c76_type,type,
c76: $i ).
tff(c75_type,type,
c75: $i ).
tff(p59_type,type,
p59: ( $i * $i ) > $o ).
tff(f35_type,type,
f35: ( $i * $i ) > $i ).
tff(c73_type,type,
c73: $i ).
tff(f38_type,type,
f38: ( $i * $i ) > $i ).
tff(c72_type,type,
c72: $i ).
tff(p9_type,type,
p9: ( $i * $i ) > $o ).
tff(p40_type,type,
p40: ( $i * $i ) > $o ).
tff(c64_type,type,
c64: $i ).
tff(p56_type,type,
p56: ( $i * $i ) > $o ).
tff(p57_type,type,
p57: ( $i * $i ) > $o ).
tff(f26_type,type,
f26: ( $i * $i ) > $i ).
tff(f41_type,type,
f41: ( $i * $i ) > $i ).
tff(c78_type,type,
c78: $i ).
tff(f28_type,type,
f28: ( $i * $i ) > $i ).
tff(c71_type,type,
c71: $i ).
tff(1,plain,
^ [X7: $i] :
refl(
( p12(X7,X7)
<=> p12(X7,X7) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X7: $i] : p12(X7,X7)
<=> ! [X7: $i] : p12(X7,X7) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X7: $i] : p12(X7,X7)
<=> ! [X7: $i] : p12(X7,X7) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X7: $i] : p12(X7,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_34) ).
tff(5,plain,
! [X7: $i] : p12(X7,X7),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X7: $i] : p12(X7,X7),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X7: $i] : p12(X7,X7),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X7: $i] : p12(X7,X7)
| p12(f17(c66,c67),f17(c66,c67)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p12(f17(c66,c67),f17(c66,c67)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X17: $i,X18: $i] :
refl(
( ( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
<=> ( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
<=> ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
<=> ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X17: $i,X18: $i] :
rewrite(
( ( p13(X17,f23(c74,X18))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| ~ p59(f38(c72,X18),f35(c73,X17)) )
<=> ( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X17: $i,X18: $i] :
( p13(X17,f23(c74,X18))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| ~ p59(f38(c72,X18),f35(c73,X17)) )
<=> ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X17: $i,X18: $i] :
( p13(X17,f23(c74,X18))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| ~ p59(f38(c72,X18),f35(c73,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13_105) ).
tff(16,plain,
! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
<=> ~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p58_80) ).
tff(22,plain,
~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( p59(f38(c72,c77),f35(c73,c68))
<=> p59(f38(c72,c77),f35(c73,c68)) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
p59(f38(c72,c77),f35(c73,c68)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p59_35) ).
tff(25,plain,
p59(f38(c72,c77),f35(c73,c68)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| ~ p59(f38(c72,c77),f35(c73,c68))
| p13(c68,f23(c74,c77)) )
<=> ( ~ ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| ~ p59(f38(c72,c77),f35(c73,c68))
| p13(c68,f23(c74,c77)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ~ p59(f38(c72,c77),f35(c73,c68))
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| p13(c68,f23(c74,c77)) )
<=> ( p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| ~ p59(f38(c72,c77),f35(c73,c68))
| p13(c68,f23(c74,c77)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
| ~ p59(f38(c72,c77),f35(c73,c68))
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| p13(c68,f23(c74,c77)) )
<=> ( ~ ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| ~ p59(f38(c72,c77),f35(c73,c68))
| p13(c68,f23(c74,c77)) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
| ~ p59(f38(c72,c77),f35(c73,c68))
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| p13(c68,f23(c74,c77)) )
<=> ( ~ ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| ~ p59(f38(c72,c77),f35(c73,c68))
| p13(c68,f23(c74,c77)) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
| ~ p59(f38(c72,c77),f35(c73,c68))
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| p13(c68,f23(c74,c77)) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [X17: $i,X18: $i] :
( ~ p59(f38(c72,X18),f35(c73,X17))
| p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
| p13(X17,f23(c74,X18)) )
| p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
| ~ p59(f38(c72,c77),f35(c73,c68))
| p13(c68,f23(c74,c77)) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
p13(c68,f23(c74,c77)),
inference(unit_resolution,[status(thm)],[31,25,22,19]) ).
tff(33,plain,
^ [X6: $i,X4: $i,X3: $i,X5: $i] :
refl(
( ( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) )
<=> ( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) )
<=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) )
<=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [X6: $i,X4: $i,X3: $i,X5: $i] :
trans(
monotonicity(
rewrite(
( ( p10(f14(X3,X4),f14(X5,X6))
| ~ p12(X3,X5) )
<=> ( ~ p12(X3,X5)
| p10(f14(X3,X4),f14(X5,X6)) ) )),
( ( p10(f14(X3,X4),f14(X5,X6))
| ~ p12(X3,X5)
| ~ p13(X4,X6) )
<=> ( ~ p12(X3,X5)
| p10(f14(X3,X4),f14(X5,X6))
| ~ p13(X4,X6) ) )),
rewrite(
( ( ~ p12(X3,X5)
| p10(f14(X3,X4),f14(X5,X6))
| ~ p13(X4,X6) )
<=> ( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ) )),
( ( p10(f14(X3,X4),f14(X5,X6))
| ~ p12(X3,X5)
| ~ p13(X4,X6) )
<=> ( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( p10(f14(X3,X4),f14(X5,X6))
| ~ p12(X3,X5)
| ~ p13(X4,X6) )
<=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [X6: $i,X4: $i,X3: $i,X5: $i] :
( p10(f14(X3,X4),f14(X5,X6))
| ~ p12(X3,X5)
| ~ p13(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_81) ).
tff(39,plain,
! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) )
| ~ p12(f17(c66,c67),f17(c66,c67))
| ~ p13(c68,f23(c74,c77))
| p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))) )
<=> ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) )
| ~ p12(f17(c66,c67),f17(c66,c67))
| ~ p13(c68,f23(c74,c77))
| p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) )
| ~ p12(f17(c66,c67),f17(c66,c67))
| ~ p13(c68,f23(c74,c77))
| p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
( ~ p12(X3,X5)
| ~ p13(X4,X6)
| p10(f14(X3,X4),f14(X5,X6)) )
| ~ p12(f17(c66,c67),f17(c66,c67))
| ~ p13(c68,f23(c74,c77))
| p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))),
inference(unit_resolution,[status(thm)],[45,42,32,9]) ).
tff(47,plain,
^ [X210: $i] :
refl(
( p9(X210,X210)
<=> p9(X210,X210) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X210: $i] : p9(X210,X210)
<=> ! [X210: $i] : p9(X210,X210) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X210: $i] : p9(X210,X210)
<=> ! [X210: $i] : p9(X210,X210) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
! [X210: $i] : p9(X210,X210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_2) ).
tff(51,plain,
! [X210: $i] : p9(X210,X210),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X210: $i] : p9(X210,X210),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X210: $i] : p9(X210,X210),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [X210: $i] : p9(X210,X210)
| p9(c65,c65) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
p9(c65,c65),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
^ [X122: $i,X124: $i,X121: $i,X123: $i] :
refl(
( ( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) )
<=> ( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) )
<=> ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) )
<=> ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
^ [X122: $i,X124: $i,X121: $i,X123: $i] :
trans(
monotonicity(
rewrite(
( ( p4(f11(X121,X122),f11(X123,X124))
| ~ p10(X122,X124) )
<=> ( ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ) )),
( ( p4(f11(X121,X122),f11(X123,X124))
| ~ p10(X122,X124)
| ~ p9(X121,X123) )
<=> ( ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124))
| ~ p9(X121,X123) ) )),
rewrite(
( ( ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124))
| ~ p9(X121,X123) )
<=> ( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ) )),
( ( p4(f11(X121,X122),f11(X123,X124))
| ~ p10(X122,X124)
| ~ p9(X121,X123) )
<=> ( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( p4(f11(X121,X122),f11(X123,X124))
| ~ p10(X122,X124)
| ~ p9(X121,X123) )
<=> ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [X122: $i,X124: $i,X121: $i,X123: $i] :
( p4(f11(X121,X122),f11(X123,X124))
| ~ p10(X122,X124)
| ~ p9(X121,X123) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_87) ).
tff(62,plain,
! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) )
| ~ p9(c65,c65)
| ~ p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77)))
| p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))) )
<=> ( ~ ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) )
| ~ p9(c65,c65)
| ~ p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77)))
| p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) )
| ~ p9(c65,c65)
| ~ p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77)))
| p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [X122: $i,X124: $i,X121: $i,X123: $i] :
( ~ p9(X121,X123)
| ~ p10(X122,X124)
| p4(f11(X121,X122),f11(X123,X124)) )
| ~ p9(c65,c65)
| ~ p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77)))
| p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))),
inference(unit_resolution,[status(thm)],[68,65,55,46]) ).
tff(70,plain,
^ [X129: $i] :
refl(
( p40(X129,X129)
<=> p40(X129,X129) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X129: $i] : p40(X129,X129)
<=> ! [X129: $i] : p40(X129,X129) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X129: $i] : p40(X129,X129)
<=> ! [X129: $i] : p40(X129,X129) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
! [X129: $i] : p40(X129,X129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p40_14) ).
tff(74,plain,
! [X129: $i] : p40(X129,X129),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [X129: $i] : p40(X129,X129),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X129: $i] : p40(X129,X129),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [X129: $i] : p40(X129,X129)
| p40(c64,c64) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
p40(c64,c64),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
^ [X188: $i,X186: $i,X187: $i] :
refl(
( ( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) )
<=> ( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) )
<=> ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) )
<=> ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
^ [X188: $i,X186: $i,X187: $i] :
rewrite(
( ( p57(f26(f28(c71,X186),X187),X188)
| ~ p57(f26(X186,X187),X188) )
<=> ( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [X188: $i,X186: $i,X187: $i] :
( p57(f26(f28(c71,X186),X187),X188)
| ~ p57(f26(X186,X187),X188) )
<=> ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,axiom,
! [X188: $i,X186: $i,X187: $i] :
( p57(f26(f28(c71,X186),X187),X188)
| ~ p57(f26(X186,X187),X188) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p57_74) ).
tff(85,plain,
! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
( ~ p57(f26(f28(c71,f41(c78,c64)),c67),c77)
<=> ~ p57(f26(f28(c71,f41(c78,c64)),c67),c77) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
~ p57(f26(f28(c71,f41(c78,c64)),c67),c77),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p57_39) ).
tff(91,plain,
~ p57(f26(f28(c71,f41(c78,c64)),c67),c77),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ( ~ ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) )
| ~ p57(f26(f41(c78,c64),c67),c77)
| p57(f26(f28(c71,f41(c78,c64)),c67),c77) )
<=> ( ~ ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) )
| ~ p57(f26(f41(c78,c64),c67),c77)
| p57(f26(f28(c71,f41(c78,c64)),c67),c77) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) )
| ~ p57(f26(f41(c78,c64),c67),c77)
| p57(f26(f28(c71,f41(c78,c64)),c67),c77) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X188: $i,X186: $i,X187: $i] :
( ~ p57(f26(X186,X187),X188)
| p57(f26(f28(c71,X186),X187),X188) )
| ~ p57(f26(f41(c78,c64),c67),c77)
| p57(f26(f28(c71,f41(c78,c64)),c67),c77) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
~ p57(f26(f41(c78,c64),c67),c77),
inference(unit_resolution,[status(thm)],[94,91,88]) ).
tff(96,plain,
^ [X179: $i,X181: $i,X180: $i] :
refl(
( ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) )
<=> ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) )
<=> ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) )
<=> ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
^ [X179: $i,X181: $i,X180: $i] :
rewrite(
( ( p57(f26(f41(c78,X181),X179),X180)
| ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181) )
<=> ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [X179: $i,X181: $i,X180: $i] :
( p57(f26(f41(c78,X181),X179),X180)
| ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181) )
<=> ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [X179: $i,X181: $i,X180: $i] :
( p57(f26(f41(c78,X181),X179),X180)
| ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p57_101) ).
tff(102,plain,
! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) )
| ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64)
| p57(f26(f41(c78,c64),c67),c77) )
<=> ( ~ ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) )
| ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64)
| p57(f26(f41(c78,c64),c67),c77) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ~ ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) )
| ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64)
| p57(f26(f41(c78,c64),c67),c77) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [X179: $i,X181: $i,X180: $i] :
( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
| p57(f26(f41(c78,X181),X179),X180) )
| ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64)
| p57(f26(f41(c78,c64),c67),c77) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64),
inference(unit_resolution,[status(thm)],[108,105,95]) ).
tff(110,plain,
^ [X175: $i,X176: $i,X178: $i,X177: $i] :
refl(
( ( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) )
<=> ( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) )
<=> ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) )
<=> ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
^ [X175: $i,X176: $i,X178: $i,X177: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p56(X175,X176)
| ~ p40(X178,X176) )
<=> ( ~ p40(X178,X176)
| p56(X175,X176) ) )),
( ( p56(X175,X176)
| ~ p40(X178,X176)
| ~ p56(X177,X178) )
<=> ( ~ p40(X178,X176)
| p56(X175,X176)
| ~ p56(X177,X178) ) )),
rewrite(
( ( ~ p40(X178,X176)
| p56(X175,X176)
| ~ p56(X177,X178) )
<=> ( ~ p40(X178,X176)
| ~ p56(X177,X178)
| p56(X175,X176) ) )),
( ( p56(X175,X176)
| ~ p40(X178,X176)
| ~ p56(X177,X178) )
<=> ( ~ p40(X178,X176)
| ~ p56(X177,X178)
| p56(X175,X176) ) )),
( ( p56(X175,X176)
| ~ p40(X178,X176)
| ~ p56(X177,X178)
| ~ p4(X177,X175) )
<=> ( ~ p40(X178,X176)
| ~ p56(X177,X178)
| p56(X175,X176)
| ~ p4(X177,X175) ) )),
rewrite(
( ( ~ p40(X178,X176)
| ~ p56(X177,X178)
| p56(X175,X176)
| ~ p4(X177,X175) )
<=> ( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ) )),
( ( p56(X175,X176)
| ~ p40(X178,X176)
| ~ p56(X177,X178)
| ~ p4(X177,X175) )
<=> ( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( p56(X175,X176)
| ~ p40(X178,X176)
| ~ p56(X177,X178)
| ~ p4(X177,X175) )
<=> ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,axiom,
! [X175: $i,X176: $i,X178: $i,X177: $i] :
( p56(X175,X176)
| ~ p40(X178,X176)
| ~ p56(X177,X178)
| ~ p4(X177,X175) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p56_76) ).
tff(116,plain,
! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) ),
inference(modus_ponens,[status(thm)],[118,111]) ).
tff(120,plain,
( p56(f11(c65,f14(f17(c66,c67),c68)),c64)
<=> p56(f11(c65,f14(f17(c66,c67),c68)),c64) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
p56(f11(c65,f14(f17(c66,c67),c68)),c64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p56_38) ).
tff(122,plain,
p56(f11(c65,f14(f17(c66,c67),c68)),c64),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ( ~ ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) )
| ~ p40(c64,c64)
| ~ p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77))))
| ~ p56(f11(c65,f14(f17(c66,c67),c68)),c64)
| p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) )
<=> ( ~ ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) )
| ~ p40(c64,c64)
| ~ p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77))))
| ~ p56(f11(c65,f14(f17(c66,c67),c68)),c64)
| p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) )
| ~ p40(c64,c64)
| ~ p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77))))
| ~ p56(f11(c65,f14(f17(c66,c67),c68)),c64)
| p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [X175: $i,X176: $i,X178: $i,X177: $i] :
( ~ p40(X178,X176)
| ~ p4(X177,X175)
| ~ p56(X177,X178)
| p56(X175,X176) )
| ~ p40(c64,c64)
| ~ p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77))))
| ~ p56(f11(c65,f14(f17(c66,c67),c68)),c64)
| p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
$false,
inference(unit_resolution,[status(thm)],[125,122,119,109,78,69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN713-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Sep 5 06:39:35 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.47/0.54 % SZS status Unsatisfiable
% 0.47/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------