%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV000^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 Oct 9 02:56:05 PM UTC 2025
% Result : Theorem 23.94s 24.06s
% Output : Proof 23.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 62 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 349 ( 80 equ; 0 cnn)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 639 ( 98 ~; 52 |; 8 &; 440 @)
% ( 0 <=>; 38 =>; 3 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 18 con; 0-2 aty)
% Number of variables : 145 ( 0 ^; 145 !; 0 ?; 145 :)
% Comments :
%------------------------------------------------------------------------------
thf(cMODULAR_EQUIV_THM_pme,conjecture,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ( ( ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) )
= ( ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ( ( ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) )
= ( ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cMODULAR_EQUIV_THM_pme]) ).
thf(ax17,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax17) ).
thf(ax18,axiom,
~ p1,
file('<stdin>',ax18) ).
thf(ax16,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax16) ).
thf(ax15,axiom,
( p3
| ~ p4 ),
file('<stdin>',ax15) ).
thf(nax4,axiom,
( p4
<= ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( f__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__1 @ X1 @ X2 ) @ X3 )
= ( f__1 @ X1 @ ( f__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__0 @ ( f__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( f__1 @ ( f__0 @ X1 @ X2 ) @ X2 )
= X2 ) ) ),
file('<stdin>',nax4) ).
thf(ax14,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax14) ).
thf(nax15,axiom,
( p15
<= ! [X1: a,X2: a,X3: a] :
( ( f__0 @ X1 @ ( f__1 @ X2 @ ( f__0 @ X1 @ X3 ) ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) ) ),
file('<stdin>',nax15) ).
thf(pax14,axiom,
( p14
=> ! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ X1 @ X3 )
= X3 )
=> ( ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ X3 ) ) ) ),
file('<stdin>',pax14) ).
thf(ax4,axiom,
( p5
| p14
| p15 ),
file('<stdin>',ax4) ).
thf(pax15,axiom,
( p15
=> ! [X1: a,X2: a,X3: a] :
( ( f__0 @ X1 @ ( f__1 @ X2 @ ( f__0 @ X1 @ X3 ) ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) ) ),
file('<stdin>',pax15) ).
thf(nax18,axiom,
( p18
<= ! [X1: a,X2: a] :
( ( ( f__0 @ f__2 @ X2 )
= X2 )
=> ( ( f__0 @ f__2 @ ( f__1 @ X1 @ X2 ) )
= ( f__1 @ ( f__0 @ f__2 @ X1 ) @ X2 ) ) ) ),
file('<stdin>',nax18) ).
thf(ax3,axiom,
( p5
| ~ p14
| ~ p15 ),
file('<stdin>',ax3) ).
thf(ax0,axiom,
( p14
| ~ p18 ),
file('<stdin>',ax0) ).
thf(c_0_13,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax17]) ).
thf(c_0_14,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax18]) ).
thf(c_0_15,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax16]) ).
thf(c_0_16,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
( p3
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax15]) ).
thf(c_0_19,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,plain,
~ p2,
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,plain,
! [X120: a,X121: a,X122: a,X123: a,X124: a,X125: a,X126: a,X127: a,X128: a,X129: a,X130: a,X131: a,X132: a,X133: a,X134: a,X135: a] :
( ( ( ( f__0 @ X120 @ X120 )
= X120 )
| p4 )
& ( ( ( f__1 @ X121 @ X121 )
= X121 )
| p4 )
& ( ( ( f__0 @ ( f__0 @ X122 @ X123 ) @ X124 )
= ( f__0 @ X122 @ ( f__0 @ X123 @ X124 ) ) )
| p4 )
& ( ( ( f__1 @ ( f__1 @ X125 @ X126 ) @ X127 )
= ( f__1 @ X125 @ ( f__1 @ X126 @ X127 ) ) )
| p4 )
& ( ( ( f__0 @ X128 @ X129 )
= ( f__0 @ X129 @ X128 ) )
| p4 )
& ( ( ( f__1 @ X130 @ X131 )
= ( f__1 @ X131 @ X130 ) )
| p4 )
& ( ( ( f__0 @ ( f__1 @ X132 @ X133 ) @ X133 )
= X133 )
| p4 )
& ( ( ( f__1 @ ( f__0 @ X134 @ X135 ) @ X135 )
= X135 )
| p4 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax4])])])])]) ).
thf(c_0_22,plain,
( p3
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,plain,
~ p3,
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_24,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax14]) ).
thf(c_0_25,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| p4 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,plain,
~ p4,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_27,plain,
! [X1: a] :
( ( ( f__0 @ X1 @ X1 )
= X1 )
| p4 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_28,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,plain,
( ( ( f__0 @ esk29_0 @ ( f__1 @ esk30_0 @ ( f__0 @ esk29_0 @ esk31_0 ) ) )
!= ( f__1 @ ( f__0 @ esk29_0 @ esk30_0 ) @ ( f__0 @ esk29_0 @ esk31_0 ) ) )
| p15 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax15])])])]) ).
thf(c_0_30,plain,
! [X66: a,X67: a,X68: a] :
( ~ p14
| ( ( f__0 @ X66 @ X68 )
!= X68 )
| ( ( f__0 @ X66 @ ( f__1 @ X67 @ X68 ) )
= ( f__1 @ ( f__0 @ X66 @ X67 ) @ X68 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax14])])]) ).
thf(c_0_31,plain,
! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_32,plain,
! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_27,c_0_26]) ).
thf(c_0_33,plain,
( p5
| p14
| p15 ),
inference(split_conjunct,[status(thm)],[ax4]) ).
thf(c_0_34,plain,
~ p5,
inference(sr,[status(thm)],[c_0_28,c_0_23]) ).
thf(c_0_35,plain,
! [X60: a,X61: a,X62: a] :
( ~ p15
| ( ( f__0 @ X60 @ ( f__1 @ X61 @ ( f__0 @ X60 @ X62 ) ) )
= ( f__1 @ ( f__0 @ X60 @ X61 ) @ ( f__0 @ X60 @ X62 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax15])])]) ).
thf(c_0_36,plain,
( p15
| ( ( f__0 @ esk29_0 @ ( f__1 @ esk30_0 @ ( f__0 @ esk29_0 @ esk31_0 ) ) )
!= ( f__1 @ ( f__0 @ esk29_0 @ esk30_0 ) @ ( f__0 @ esk29_0 @ esk31_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_37,plain,
! [X1: a,X3: a,X2: a] :
( ( ( f__0 @ X1 @ ( f__1 @ X3 @ X2 ) )
= ( f__1 @ ( f__0 @ X1 @ X3 ) @ X2 ) )
| ~ p14
| ( ( f__0 @ X1 @ X2 )
!= X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,plain,
! [X1: a,X2: a] :
( ( f__0 @ X1 @ ( f__0 @ X1 @ X2 ) )
= ( f__0 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_39,plain,
( p15
| p14 ),
inference(sr,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_40,plain,
( ( ( ( f__0 @ f__2 @ esk14_0 )
= esk14_0 )
| p18 )
& ( ( ( f__0 @ f__2 @ ( f__1 @ esk13_0 @ esk14_0 ) )
!= ( f__1 @ ( f__0 @ f__2 @ esk13_0 ) @ esk14_0 ) )
| p18 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax18])])])])]) ).
thf(c_0_41,plain,
! [X2: a,X1: a] :
( ( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) )
| p4 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_42,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ X1 @ ( f__1 @ X2 @ ( f__0 @ X1 @ X3 ) ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) )
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_43,plain,
p15,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),c_0_39]) ).
thf(c_0_44,plain,
( p5
| ~ p14
| ~ p15 ),
inference(fof_simplification,[status(thm)],[ax3]) ).
thf(c_0_45,plain,
( p18
| ( ( f__0 @ f__2 @ ( f__1 @ esk13_0 @ esk14_0 ) )
!= ( f__1 @ ( f__0 @ f__2 @ esk13_0 ) @ esk14_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_46,plain,
! [X2: a,X1: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ),
inference(sr,[status(thm)],[c_0_41,c_0_26]) ).
thf(c_0_47,plain,
! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) )
= ( f__0 @ X1 @ ( f__1 @ X2 @ ( f__0 @ X1 @ X3 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_48,plain,
( ( ( f__0 @ f__2 @ esk14_0 )
= esk14_0 )
| p18 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_49,plain,
( p5
| ~ p14
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_50,plain,
( p14
| ~ p18 ),
inference(fof_simplification,[status(thm)],[ax0]) ).
thf(c_0_51,plain,
( p18
| ( ( f__1 @ esk14_0 @ ( f__0 @ f__2 @ esk13_0 ) )
!= ( f__0 @ f__2 @ ( f__1 @ esk14_0 @ esk13_0 ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_46]) ).
thf(c_0_52,plain,
! [X1: a] :
( ( ( f__1 @ esk14_0 @ ( f__0 @ f__2 @ X1 ) )
= ( f__0 @ f__2 @ ( f__1 @ X1 @ esk14_0 ) ) )
| p18 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_46]) ).
thf(c_0_53,plain,
( ~ p14
| ~ p15 ),
inference(sr,[status(thm)],[c_0_49,c_0_34]) ).
thf(c_0_54,plain,
( p14
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_55,plain,
p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_46])]) ).
thf(c_0_56,plain,
~ p14,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_43])]) ).
thf(c_0_57,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),c_0_56]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ( ( ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) )
= ( ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SEV000^5 : TPTP v9.2.0. Released v4.0.0.
% 0.14/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 19:08:53 EDT 2025
% 0.22/0.36 % CPUTime :
% 23.94/24.06 % SZS status Theorem
% 23.94/24.06 % Mode: mode371
% 23.94/24.06 % Inferences: 12
% 23.94/24.06 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------