%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM018+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:00:59 AM UTC 2025
% Result : Theorem 0.24s 0.45s
% Output : Proof 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 49 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 266 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 341 ( 153 ~; 124 |; 24 &)
% ( 28 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 76 !; 24 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
tff(aNormalFormOfIn0_type,type,
aNormalFormOfIn0: ( $i * $i * $i ) > $o ).
tff(xR_type,type,
xR: $i ).
tff(xw_type,type,
xw: $i ).
tff(tptp_fun_W2_11_type,type,
tptp_fun_W2_11: ( $i * $i ) > $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(isTerminating0_type,type,
isTerminating0: $i > $o ).
tff(isLocallyConfluent0_type,type,
isLocallyConfluent0: $i > $o ).
tff(aRewritingSystem0_type,type,
aRewritingSystem0: $i > $o ).
tff(sdtmndtasgtdt0_type,type,
sdtmndtasgtdt0: ( $i * $i * $i ) > $o ).
tff(xu_type,type,
xu: $i ).
tff(xv_type,type,
xv: $i ).
tff(1,plain,
( isTerminating0(xR)
<=> isTerminating0(xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
tff(3,plain,
isTerminating0(xR),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
isTerminating0(xR),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aRewritingSystem0(xR)
<=> aRewritingSystem0(xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
tff(7,plain,
aRewritingSystem0(xR),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [W0: $i] :
refl(( ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) ),
inference(transitivity,[status(thm)],[11,9]) ).
tff(13,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
<=> ~ ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0) ) )),
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
<=> ~ ~ ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0) ) )),
rewrite(( ~ ~ ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0) )
<=> ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0) ) )),
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
<=> ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0) ) )),
( ( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) )),
rewrite(( ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) )),
( ( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
<=> ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) )
<=> ! [W0: $i] :
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElement0(W1)
=> ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) )
<=> ( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ))),
( ! [W1: $i] :
( aElement0(W1)
=> ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) )
<=> ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) )),
( ( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) )
<=> ( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ) )),
rewrite(( ( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) )
<=> ( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ) )),
( ( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) )
<=> ( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i] :
( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) )
<=> ! [W0: $i] :
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [W0: $i] :
( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermNF) ).
tff(19,plain,
! [W0: $i] :
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [W0: $i] :
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| ? [W2: $i] : aNormalFormOfIn0(W2,W1,W0) ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [W0: $i] :
( ~ ( aRewritingSystem0(W0)
& isTerminating0(W0) )
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) ),
inference(modus_ponens,[status(thm)],[22,12]) ).
tff(24,plain,
( ( ~ ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
| ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) ) )
<=> ( ~ ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
| ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
| ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [W0: $i] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,W0),W1,W0) ) )
| ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) ),
inference(unit_resolution,[status(thm)],[26,23,7,4]) ).
tff(28,plain,
( aElement0(xw)
<=> aElement0(xw) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
tff(30,plain,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw) ),
inference(and_elim,[status(thm)],[29]) ).
tff(31,plain,
aElement0(xw),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
aElement0(xw),
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,plain,
( ( ~ ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) )
| ~ aElement0(xw)
| aNormalFormOfIn0(tptp_fun_W2_11(xw,xR),xw,xR) )
<=> ( ~ ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) )
| ~ aElement0(xw)
| aNormalFormOfIn0(tptp_fun_W2_11(xw,xR),xw,xR) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) )
| ~ aElement0(xw)
| aNormalFormOfIn0(tptp_fun_W2_11(xw,xR),xw,xR) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [W1: $i] :
( ~ aElement0(W1)
| aNormalFormOfIn0(tptp_fun_W2_11(W1,xR),W1,xR) )
| ~ aElement0(xw)
| aNormalFormOfIn0(tptp_fun_W2_11(xw,xR),xw,xR) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
aNormalFormOfIn0(tptp_fun_W2_11(xw,xR),xw,xR),
inference(unit_resolution,[status(thm)],[35,32,27]) ).
tff(37,plain,
^ [W0: $i] :
refl(( ~ aNormalFormOfIn0(W0,xw,xR)
<=> ~ aNormalFormOfIn0(W0,xw,xR) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [W0: $i] : ~ aNormalFormOfIn0(W0,xw,xR)
<=> ! [W0: $i] : ~ aNormalFormOfIn0(W0,xw,xR) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ~ ? [W0: $i] : aNormalFormOfIn0(W0,xw,xR)
<=> ~ ? [W0: $i] : aNormalFormOfIn0(W0,xw,xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
~ ? [W0: $i] : aNormalFormOfIn0(W0,xw,xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(41,plain,
~ ? [W0: $i] : aNormalFormOfIn0(W0,xw,xR),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ ? [W0: $i] : aNormalFormOfIn0(W0,xw,xR),
inference(modus_ponens,[status(thm)],[41,39]) ).
tff(43,plain,
~ ? [W0: $i] : aNormalFormOfIn0(W0,xw,xR),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
~ ? [W0: $i] : aNormalFormOfIn0(W0,xw,xR),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
^ [W0: $i] : refl($oeq(~ aNormalFormOfIn0(W0,xw,xR),~ aNormalFormOfIn0(W0,xw,xR))),
inference(bind,[status(th)],[]) ).
tff(46,plain,
! [W0: $i] : ~ aNormalFormOfIn0(W0,xw,xR),
inference(nnf-neg,[status(sab)],[44,45]) ).
tff(47,plain,
! [W0: $i] : ~ aNormalFormOfIn0(W0,xw,xR),
inference(modus_ponens,[status(thm)],[46,38]) ).
tff(48,plain,
( ~ ! [W0: $i] : ~ aNormalFormOfIn0(W0,xw,xR)
| ~ aNormalFormOfIn0(tptp_fun_W2_11(xw,xR),xw,xR) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,47,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : COM018+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n002.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Jun 19 12:22:46 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.24/0.45 % SZS status Theorem
% 0.24/0.45 % SZS output start Proof
% See solution above
% 0.24/0.46 % E exiting
%------------------------------------------------------------------------------