%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN621-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:39:42 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 56 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 219 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 252 ( 100 ~; 128 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-4 aty)
% Number of variables : 169 ( 156 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
tff(p21_type,type,
p21: ( $i * $i ) > $o ).
tff(f5_type,type,
f5: $i > $i ).
tff(f6_type,type,
f6: ( $i * $i ) > $i ).
tff(f20_type,type,
f20: ( $i * $i * $i * $i ) > $i ).
tff(c27_type,type,
c27: $i ).
tff(c26_type,type,
c26: $i ).
tff(c23_type,type,
c23: $i ).
tff(c25_type,type,
c25: $i ).
tff(f9_type,type,
f9: ( $i * $i * $i ) > $i ).
tff(c28_type,type,
c28: $i ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(f12_type,type,
f12: ( $i * $i ) > $i ).
tff(p22_type,type,
p22: ( $i * $i ) > $o ).
tff(f14_type,type,
f14: $i > $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f3_type,type,
f3: $i > $i ).
tff(c24_type,type,
c24: $i ).
tff(f15_type,type,
f15: ( $i * $i ) > $i ).
tff(f16_type,type,
f16: $i > $i ).
tff(f17_type,type,
f17: $i > $i ).
tff(f18_type,type,
f18: $i > $i ).
tff(f19_type,type,
f19: ( $i * $i ) > $i ).
tff(1,plain,
^ [X17: $i,X16: $i,X18: $i,X15: $i] :
refl(( ( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) )
<=> ( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) )
<=> ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) )
<=> ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_28) ).
tff(5,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ p2(c23,f3(c24))
<=> ~ p2(c23,f3(c24)) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ p2(c23,f3(c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_7) ).
tff(10,plain,
~ p2(c23,f3(c24)),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) )
| p2(c23,f3(c24))
| p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26)))) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) )
| p2(c23,f3(c24))
| p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) )
| p2(c23,f3(c24))
| p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18)))) )
| p2(c23,f3(c24))
| p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26)))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26)))),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [X33: $i] :
refl(( ( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) )
<=> ( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) )
<=> ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) )
<=> ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [X33: $i] :
rewrite(( ( p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33)))
| ~ p22(X33,f14(f11(c25,f12(c23,c26)))) )
<=> ( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X33: $i] :
( p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33)))
| ~ p22(X33,f14(f11(c25,f12(c23,c26)))) )
<=> ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [X33: $i] :
( p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33)))
| ~ p22(X33,f14(f11(c25,f12(c23,c26)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_31) ).
tff(21,plain,
! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) )
| ~ p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27)))) )
<=> ( ~ ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) )
| ~ p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) )
| ~ p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [X33: $i] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) )
| ~ p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27)))) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ p22(f20(c25,c23,c26,c27),f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27)))) ),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,plain,
p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27)))),
inference(unit_resolution,[status(thm)],[28,14]) ).
tff(30,plain,
^ [X17: $i,X16: $i,X18: $i,X15: $i] :
refl(( ( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) )
<=> ( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) )
<=> ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) )
<=> ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_34) ).
tff(34,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) )
| p2(c23,f3(c24))
| p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) )
| p2(c23,f3(c24))
| p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) )
| p2(c23,f3(c24))
| p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(X15,f3(c24))
| p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24)))))) )
| p2(c23,f3(c24))
| p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),
inference(unit_resolution,[status(thm)],[39,10,36]) ).
tff(41,plain,
( ~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24))))))
<=> ~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p21_32) ).
tff(43,plain,
~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) )
<=> ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) )
<=> ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
^ [X31: $i,X32: $i,X30: $i] :
trans(monotonicity(rewrite(( ( p21(X30,X31)
| ~ p21(X30,X32) )
<=> ( ~ p21(X30,X32)
| p21(X30,X31) ) )),
( ( p21(X30,X31)
| ~ p21(X30,X32)
| ~ p21(X32,X31) )
<=> ( ~ p21(X30,X32)
| p21(X30,X31)
| ~ p21(X32,X31) ) )),
rewrite(( ( ~ p21(X30,X32)
| p21(X30,X31)
| ~ p21(X32,X31) )
<=> ( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ) )),
( ( p21(X30,X31)
| ~ p21(X30,X32)
| ~ p21(X32,X31) )
<=> ( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X31: $i,X32: $i,X30: $i] :
( p21(X30,X31)
| ~ p21(X30,X32)
| ~ p21(X32,X31) )
<=> ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [X31: $i,X32: $i,X30: $i] :
( p21(X30,X31)
| ~ p21(X30,X32)
| ~ p21(X32,X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_18) ).
tff(49,plain,
! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) )
| ~ p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24))))))
| ~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) )
<=> ( ~ ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) )
| ~ p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24))))))
| ~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) )
| ~ p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24))))))
| ~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [X31: $i,X32: $i,X30: $i] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) )
| ~ p21(f5(f6(c27,f20(c25,c23,c26,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24))))))
| ~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,c27))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,52,43,40,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN621-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 12:38:52 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------