%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CSR031+5 : TPTP v9.0.0. Bugfixed v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:01:19 AM UTC 2025
% Result : Theorem 113.12s 113.35s
% Output : Proof 124.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 164 ( 86 ~; 48 |; 9 &)
% ( 18 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 10 ( 10 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(collection_type,type,
collection: $i > $o ).
tff(c_tptptptpcol_16_8398_type,type,
c_tptptptpcol_16_8398: $i ).
tff(individual_type,type,
individual: $i > $o ).
tff(disjointwith_type,type,
disjointwith: ( $i * $i ) > $o ).
tff(c_tptpcol_16_18488_type,type,
c_tptpcol_16_18488: $i ).
tff(1,plain,
( individual(c_tptptptpcol_16_8398)
<=> individual(c_tptptptpcol_16_8398) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
individual(c_tptptptpcol_16_8398),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+4.ax',ax4_128360) ).
tff(3,plain,
individual(c_tptptptpcol_16_8398),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [OBJ: $i] :
refl(( ( ~ collection(OBJ)
| ~ individual(OBJ) )
<=> ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
<=> ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [OBJ: $i] :
trans(monotonicity(rewrite(( ( collection(OBJ)
& individual(OBJ) )
<=> ~ ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
( ~ ( collection(OBJ)
& individual(OBJ) )
<=> ~ ~ ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
rewrite(( ~ ~ ( ~ collection(OBJ)
| ~ individual(OBJ) )
<=> ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
( ~ ( collection(OBJ)
& individual(OBJ) )
<=> ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) )
<=> ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) )
<=> ! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+4.ax',ax4_117519) ).
tff(10,plain,
! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
| ~ collection(c_tptptptpcol_16_8398)
| ~ individual(c_tptptptpcol_16_8398) )
<=> ( ~ ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
| ~ collection(c_tptptptpcol_16_8398)
| ~ individual(c_tptptptpcol_16_8398) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
| ~ collection(c_tptptptpcol_16_8398)
| ~ individual(c_tptptptpcol_16_8398) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
| ~ collection(c_tptptptpcol_16_8398)
| ~ individual(c_tptptptpcol_16_8398) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ collection(c_tptptptpcol_16_8398),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488)
<=> disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488)
<=> disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
~ ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query231) ).
tff(21,plain,
disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
^ [INS: $i,ARG2: $i] :
refl(( ( collection(INS)
| ~ disjointwith(INS,ARG2) )
<=> ( collection(INS)
| ~ disjointwith(INS,ARG2) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
<=> ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
<=> ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
^ [INS: $i,ARG2: $i] :
rewrite(( ( disjointwith(INS,ARG2)
=> collection(INS) )
<=> ( collection(INS)
| ~ disjointwith(INS,ARG2) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [INS: $i,ARG2: $i] :
( disjointwith(INS,ARG2)
=> collection(INS) )
<=> ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [INS: $i,ARG2: $i] :
( disjointwith(INS,ARG2)
=> collection(INS) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+4.ax',ax4_540134) ).
tff(29,plain,
! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
| collection(c_tptptptpcol_16_8398)
| ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) )
<=> ( ~ ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
| collection(c_tptptptpcol_16_8398)
| ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
| collection(c_tptptptpcol_16_8398)
| ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
| collection(c_tptptptpcol_16_8398)
| ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,32,22,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : CSR031+5 : TPTP v9.0.0. Bugfixed v3.5.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 12:32:03 EDT 2025
% 0.11/0.32 % CPUTime :
% 113.12/113.35 % SZS status Theorem
% 113.12/113.35 % SZS output start Proof
% See solution above
% 124.94/125.16 % E exiting
%------------------------------------------------------------------------------