%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO083-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:05:32 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 48
% Syntax : Number of formulae : 109 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 600 ( 49 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 766 ( 317 ~; 377 |; 0 &)
% ( 72 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 403 ( 367 !; 0 ?; 403 :)
% Comments :
%------------------------------------------------------------------------------
tff(incident_c_type,type,
incident_c: ( $i * $i ) > $o ).
tff(sk16_type,type,
sk16: $i ).
tff(ax0_sk1_type,type,
ax0_sk1: ( $i * $i ) > $i ).
tff(sum_type,type,
sum: ( $i * $i ) > $i ).
tff(sk14_type,type,
sk14: $i ).
tff(sk15_type,type,
sk15: $i ).
tff(part_of_type,type,
part_of: ( $i * $i ) > $o ).
tff(1,plain,
( ~ part_of(sum(sk14,sk15),sum(sk14,sk16))
<=> ~ part_of(sum(sk14,sk15),sum(sk14,sk16)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ part_of(sum(sk14,sk15),sum(sk14,sk16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_1_70) ).
tff(3,plain,
~ part_of(sum(sk14,sk15),sum(sk14,sk16)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,A: $i] :
refl(( ( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
<=> ( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
<=> ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
<=> ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',part_of_defn_3) ).
tff(8,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16))
| part_of(sum(sk14,sk15),sum(sk14,sk16)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16))
| part_of(sum(sk14,sk15),sum(sk14,sk16)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16))
| part_of(sum(sk14,sk15),sum(sk14,sk16)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16))
| part_of(sum(sk14,sk15),sum(sk14,sk16)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) )
<=> ( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(19,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,A)
| ( A != sum(B,C) )
| ~ incident_c(D,C) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(20,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,A)
| ( A != sum(B,C) )
| ~ incident_c(D,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ) ),
inference(transitivity,[status(thm)],[19,18]) ).
tff(21,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( ( A != sum(B,C) )
| ~ incident_c(D,C) )
<=> ( ( A != sum(B,C) )
| ~ incident_c(D,C) ) )),
( ( ( A != sum(B,C) )
| ~ incident_c(D,C)
| incident_c(D,A) )
<=> ( ( A != sum(B,C) )
| ~ incident_c(D,C)
| incident_c(D,A) ) )),
rewrite(( ( ( A != sum(B,C) )
| ~ incident_c(D,C)
| incident_c(D,A) )
<=> ( incident_c(D,A)
| ( A != sum(B,C) )
| ~ incident_c(D,C) ) )),
( ( ( A != sum(B,C) )
| ~ incident_c(D,C)
| incident_c(D,A) )
<=> ( incident_c(D,A)
| ( A != sum(B,C) )
| ~ incident_c(D,C) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,C)
| incident_c(D,A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,A)
| ( A != sum(B,C) )
| ~ incident_c(D,C) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,C)
| incident_c(D,A) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,C)
| incident_c(D,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',sum_defn_6) ).
tff(25,plain,
! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[25,17]) ).
tff(27,plain,
! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[27,16]) ).
tff(29,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,C)
| incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16),
inference(unit_resolution,[status(thm)],[31,28,14]) ).
tff(33,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) )
<=> ( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(37,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,A)
| ( A != sum(B,C) ) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(38,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,A)
| ( A != sum(B,C) ) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ) ),
inference(transitivity,[status(thm)],[37,36]) ).
tff(39,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( ( A != sum(B,C) )
| ~ incident_c(D,B) )
<=> ( ~ incident_c(D,B)
| ( A != sum(B,C) ) ) )),
( ( ( A != sum(B,C) )
| ~ incident_c(D,B)
| incident_c(D,A) )
<=> ( ~ incident_c(D,B)
| ( A != sum(B,C) )
| incident_c(D,A) ) )),
rewrite(( ( ~ incident_c(D,B)
| ( A != sum(B,C) )
| incident_c(D,A) )
<=> ( ~ incident_c(D,B)
| incident_c(D,A)
| ( A != sum(B,C) ) ) )),
( ( ( A != sum(B,C) )
| ~ incident_c(D,B)
| incident_c(D,A) )
<=> ( ~ incident_c(D,B)
| incident_c(D,A)
| ( A != sum(B,C) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,B)
| incident_c(D,A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,A)
| ( A != sum(B,C) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,B)
| incident_c(D,A) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,B)
| incident_c(D,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',sum_defn_5) ).
tff(43,plain,
! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[43,35]) ).
tff(45,plain,
! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[45,34]) ).
tff(47,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ incident_c(D,B)
| incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14),
inference(unit_resolution,[status(thm)],[49,46,14]) ).
tff(51,plain,
^ [B: $i,A: $i] :
refl(( ( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
<=> ( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
<=> ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
<=> ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [B: $i,A: $i] :
rewrite(( ( incident_c(ax0_sk1(A,B),A)
| part_of(A,B) )
<=> ( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [B: $i,A: $i] :
( incident_c(ax0_sk1(A,B),A)
| part_of(A,B) )
<=> ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [B: $i,A: $i] :
( incident_c(ax0_sk1(A,B),A)
| part_of(A,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',part_of_defn_2) ).
tff(57,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sum(sk14,sk15),sum(sk14,sk16))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)) )
<=> ( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sum(sk14,sk15),sum(sk14,sk16))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sum(sk14,sk15),sum(sk14,sk16))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sum(sk14,sk15),sum(sk14,sk16))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)),
inference(unit_resolution,[status(thm)],[63,60,3]) ).
tff(65,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
<=> ( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
^ [B: $i,D: $i,C: $i] :
rewrite(( ( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,sum(B,C)) )
<=> ( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [B: $i,D: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,sum(B,C)) )
<=> ! [B: $i,D: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,sum(B,C)) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(71,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) ) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,sum(B,C)) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(72,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) ) )
<=> ! [B: $i,D: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,sum(B,C)) ) ),
inference(transitivity,[status(thm)],[71,70]) ).
tff(73,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) ) )
<=> ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ) ),
inference(transitivity,[status(thm)],[72,69]) ).
tff(74,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( A != sum(B,C) )
| ~ incident_c(D,A) )
<=> ( ~ incident_c(D,A)
| ( A != sum(B,C) ) ) )),
( ( ( A != sum(B,C) )
| ~ incident_c(D,A)
| incident_c(D,B) )
<=> ( ~ incident_c(D,A)
| ( A != sum(B,C) )
| incident_c(D,B) ) )),
rewrite(( ( ~ incident_c(D,A)
| ( A != sum(B,C) )
| incident_c(D,B) )
<=> ( incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) ) ) )),
( ( ( A != sum(B,C) )
| ~ incident_c(D,A)
| incident_c(D,B) )
<=> ( incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) ) ) )),
( ( ( A != sum(B,C) )
| ~ incident_c(D,A)
| incident_c(D,B)
| incident_c(D,C) )
<=> ( incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) )
| incident_c(D,C) ) )),
rewrite(( ( incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) )
| incident_c(D,C) )
<=> ( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) ) ) )),
( ( ( A != sum(B,C) )
| ~ incident_c(D,A)
| incident_c(D,B)
| incident_c(D,C) )
<=> ( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,A)
| incident_c(D,B)
| incident_c(D,C) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,A)
| ( A != sum(B,C) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,A)
| incident_c(D,B)
| incident_c(D,C) )
<=> ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ( A != sum(B,C) )
| ~ incident_c(D,A)
| incident_c(D,B)
| incident_c(D,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',sum_defn_4) ).
tff(78,plain,
! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[78,67]) ).
tff(80,plain,
! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) ),
inference(modus_ponens,[status(thm)],[80,66]) ).
tff(82,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)) )
<=> ( ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( incident_c(D,B)
| incident_c(D,C)
| ~ incident_c(D,sum(B,C)) )
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15))
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ),
inference(unit_resolution,[status(thm)],[87,81,64]) ).
tff(89,plain,
incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15),
inference(unit_resolution,[status(thm)],[88,50]) ).
tff(90,plain,
( part_of(sk15,sk16)
<=> part_of(sk15,sk16) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
part_of(sk15,sk16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_1_67) ).
tff(92,plain,
part_of(sk15,sk16),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
<=> ( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( ~ part_of(A,B)
| ~ incident_c(C,A) )
<=> ( ~ incident_c(C,A)
| ~ part_of(A,B) ) )),
( ( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) )
<=> ( ~ incident_c(C,A)
| ~ part_of(A,B)
| incident_c(C,B) ) )),
rewrite(( ( ~ incident_c(C,A)
| ~ part_of(A,B)
| incident_c(C,B) )
<=> ( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) )),
( ( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) )
<=> ( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) )
<=> ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [B: $i,A: $i,C: $i] :
( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',part_of_defn_1) ).
tff(99,plain,
! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| ~ part_of(sk15,sk16) )
<=> ( ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| ~ part_of(sk15,sk16) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| ~ part_of(sk15,sk16) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| ~ part_of(sk15,sk16) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
$false,
inference(unit_resolution,[status(thm)],[108,102,92,89,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO083-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 : Thu Jun 19 14:16:38 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
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------