%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP768-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:08:38 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.49s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 47
% Syntax : Number of formulae : 148 ( 111 unt; 0 typ; 0 def)
% Number of atoms : 203 ( 193 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 68 ( 22 ~; 18 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 221 ( 201 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(t_type,type,
t: ( $i * $i ) > $i ).
tff(x2_type,type,
x2: $i ).
tff(eta_type,type,
eta: $i > $i ).
tff(x0_type,type,
x0: $i ).
tff(x1_type,type,
x1: $i ).
tff(difference_type,type,
difference: ( $i * $i ) > $i ).
tff(i_type,type,
i: $i > $i ).
tff(quotient_type,type,
quotient: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( difference(A,product(A,B)) = B )
<=> ( difference(A,product(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
<=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
<=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
tff(5,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(i(x0),x0),product(product(i(x0),x0),product(t(eta(x0),x1),t(eta(x0),x2)))) = product(t(eta(x0),x1),t(eta(x0),x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
difference(product(i(x0),x0),product(product(i(x0),x0),product(t(eta(x0),x1),t(eta(x0),x2)))) = product(t(eta(x0),x1),t(eta(x0),x2)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( eta(A) = product(i(A),A) )
<=> ( eta(A) = product(i(A),A) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( eta(A) = product(i(A),A) )
<=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( eta(A) = product(i(A),A) )
<=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( eta(A) = product(i(A),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
tff(14,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
| ( eta(x0) = product(i(x0),x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
eta(x0) = product(i(x0),x0),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
product(i(x0),x0) = eta(x0),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
| ( product(eta(x0),product(x1,x2)) = product(product(eta(x0),x1),x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
product(eta(x0),product(x1,x2)) = product(product(eta(x0),x1),x2),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
product(product(eta(x0),x1),x2) = product(eta(x0),product(x1,x2)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
product(product(i(x0),x0),x1) = product(eta(x0),x1),
inference(monotonicity,[status(thm)],[19]) ).
tff(31,plain,
product(product(product(i(x0),x0),x1),x2) = product(product(eta(x0),x1),x2),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
^ [B: $i,A: $i] :
refl(( ( quotient(product(A,B),B) = A )
<=> ( quotient(product(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
tff(36,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(x2,t(eta(x0),x1)),t(eta(x0),x1)) = x2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
quotient(product(x2,t(eta(x0),x1)),t(eta(x0),x1)) = x2,
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(i(x0),x0),product(product(i(x0),x0),product(x2,t(eta(x0),x1)))) = product(x2,t(eta(x0),x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
difference(product(i(x0),x0),product(product(i(x0),x0),product(x2,t(eta(x0),x1)))) = product(x2,t(eta(x0),x1)),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
product(product(i(x0),x0),x2) = product(eta(x0),x2),
inference(monotonicity,[status(thm)],[19]) ).
tff(44,plain,
product(eta(x0),x2) = product(product(i(x0),x0),x2),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
product(product(eta(x0),x2),t(eta(x0),x1)) = product(product(product(i(x0),x0),x2),t(eta(x0),x1)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
| ( product(eta(x0),product(x2,t(eta(x0),x1))) = product(product(eta(x0),x2),t(eta(x0),x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
product(eta(x0),product(x2,t(eta(x0),x1))) = product(product(eta(x0),x2),t(eta(x0),x1)),
inference(unit_resolution,[status(thm)],[46,26]) ).
tff(48,plain,
product(product(i(x0),x0),product(x2,t(eta(x0),x1))) = product(eta(x0),product(x2,t(eta(x0),x1))),
inference(monotonicity,[status(thm)],[19]) ).
tff(49,plain,
product(product(i(x0),x0),product(x2,t(eta(x0),x1))) = product(product(product(i(x0),x0),x2),t(eta(x0),x1)),
inference(transitivity,[status(thm)],[48,47,45]) ).
tff(50,plain,
difference(product(i(x0),x0),product(product(i(x0),x0),product(x2,t(eta(x0),x1)))) = difference(product(i(x0),x0),product(product(product(i(x0),x0),x2),t(eta(x0),x1))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
difference(product(i(x0),x0),product(product(product(i(x0),x0),x2),t(eta(x0),x1))) = difference(product(i(x0),x0),product(product(i(x0),x0),product(x2,t(eta(x0),x1)))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
tff(56,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(product(i(x0),x0),product(product(product(i(x0),x0),x2),t(eta(x0),x1))) = quotient(product(x2,product(t(eta(x0),x1),product(i(x0),x0))),product(i(x0),x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
difference(product(i(x0),x0),product(product(product(i(x0),x0),x2),t(eta(x0),x1))) = quotient(product(x2,product(t(eta(x0),x1),product(i(x0),x0))),product(i(x0),x0)),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
quotient(product(x2,product(t(eta(x0),x1),product(i(x0),x0))),product(i(x0),x0)) = difference(product(i(x0),x0),product(product(product(i(x0),x0),x2),t(eta(x0),x1))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
quotient(product(x2,product(t(eta(x0),x1),product(i(x0),x0))),product(i(x0),x0)) = product(x2,t(eta(x0),x1)),
inference(transitivity,[status(thm)],[61,51,42]) ).
tff(63,plain,
quotient(quotient(product(x2,product(t(eta(x0),x1),product(i(x0),x0))),product(i(x0),x0)),t(eta(x0),x1)) = quotient(product(x2,t(eta(x0),x1)),t(eta(x0),x1)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
tff(68,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(t(eta(x0),x1),product(i(x0),x0)),product(t(eta(x0),x1),product(product(i(x0),x0),x2))) = quotient(quotient(product(x2,product(t(eta(x0),x1),product(i(x0),x0))),product(i(x0),x0)),t(eta(x0),x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
difference(product(t(eta(x0),x1),product(i(x0),x0)),product(t(eta(x0),x1),product(product(i(x0),x0),x2))) = quotient(quotient(product(x2,product(t(eta(x0),x1),product(i(x0),x0))),product(i(x0),x0)),t(eta(x0),x1)),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
quotient(product(eta(x0),x1),product(i(x0),x0)) = quotient(product(eta(x0),x1),eta(x0)),
inference(monotonicity,[status(thm)],[19]) ).
tff(74,plain,
quotient(product(eta(x0),x1),eta(x0)) = quotient(product(eta(x0),x1),product(i(x0),x0)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
^ [B: $i,A: $i] :
refl(( ( t(A,B) = quotient(product(A,B),A) )
<=> ( t(A,B) = quotient(product(A,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
<=> ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
<=> ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
tff(79,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),x1) = quotient(product(eta(x0),x1),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
t(eta(x0),x1) = quotient(product(eta(x0),x1),eta(x0)),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
t(eta(x0),x1) = quotient(product(eta(x0),x1),product(i(x0),x0)),
inference(transitivity,[status(thm)],[83,74]) ).
tff(85,plain,
product(t(eta(x0),x1),product(i(x0),x0)) = product(quotient(product(eta(x0),x1),product(i(x0),x0)),product(i(x0),x0)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
product(quotient(product(eta(x0),x1),product(i(x0),x0)),product(i(x0),x0)) = product(t(eta(x0),x1),product(i(x0),x0)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
^ [B: $i,A: $i] :
refl(( ( product(quotient(A,B),B) = A )
<=> ( product(quotient(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
tff(91,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(eta(x0),x1),product(i(x0),x0)),product(i(x0),x0)) = product(eta(x0),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
product(quotient(product(eta(x0),x1),product(i(x0),x0)),product(i(x0),x0)) = product(eta(x0),x1),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
product(eta(x0),x1) = product(quotient(product(eta(x0),x1),product(i(x0),x0)),product(i(x0),x0)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
product(eta(x0),x1) = product(t(eta(x0),x1),product(i(x0),x0)),
inference(transitivity,[status(thm)],[96,86]) ).
tff(98,plain,
difference(product(eta(x0),x1),product(t(eta(x0),x1),product(product(i(x0),x0),x2))) = difference(product(t(eta(x0),x1),product(i(x0),x0)),product(t(eta(x0),x1),product(product(i(x0),x0),x2))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
difference(product(eta(x0),x1),product(t(eta(x0),x1),product(product(i(x0),x0),x2))) = x2,
inference(transitivity,[status(thm)],[98,72,63,40]) ).
tff(100,plain,
product(eta(x0),x1) = product(product(i(x0),x0),x1),
inference(symmetry,[status(thm)],[30]) ).
tff(101,plain,
product(product(eta(x0),x1),difference(product(eta(x0),x1),product(t(eta(x0),x1),product(product(i(x0),x0),x2)))) = product(product(product(i(x0),x0),x1),x2),
inference(monotonicity,[status(thm)],[100,99]) ).
tff(102,plain,
^ [B: $i,A: $i] :
refl(( ( product(A,difference(A,B)) = B )
<=> ( product(A,difference(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
<=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
<=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,axiom,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
tff(106,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(eta(x0),x1),difference(product(eta(x0),x1),product(t(eta(x0),x1),product(product(i(x0),x0),x2)))) = product(t(eta(x0),x1),product(product(i(x0),x0),x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
product(product(eta(x0),x1),difference(product(eta(x0),x1),product(t(eta(x0),x1),product(product(i(x0),x0),x2)))) = product(t(eta(x0),x1),product(product(i(x0),x0),x2)),
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
product(t(eta(x0),x1),product(product(i(x0),x0),x2)) = product(product(eta(x0),x1),difference(product(eta(x0),x1),product(t(eta(x0),x1),product(product(i(x0),x0),x2)))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(eta(x0),x2),product(i(x0),x0)),product(i(x0),x0)) = product(eta(x0),x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
product(quotient(product(eta(x0),x2),product(i(x0),x0)),product(i(x0),x0)) = product(eta(x0),x2),
inference(unit_resolution,[status(thm)],[112,93]) ).
tff(114,plain,
quotient(product(eta(x0),x2),product(i(x0),x0)) = quotient(product(eta(x0),x2),eta(x0)),
inference(monotonicity,[status(thm)],[19]) ).
tff(115,plain,
quotient(product(eta(x0),x2),eta(x0)) = quotient(product(eta(x0),x2),product(i(x0),x0)),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),x2) = quotient(product(eta(x0),x2),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
t(eta(x0),x2) = quotient(product(eta(x0),x2),eta(x0)),
inference(unit_resolution,[status(thm)],[116,81]) ).
tff(118,plain,
t(eta(x0),x2) = quotient(product(eta(x0),x2),product(i(x0),x0)),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
product(t(eta(x0),x2),product(i(x0),x0)) = product(quotient(product(eta(x0),x2),product(i(x0),x0)),product(i(x0),x0)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
product(t(eta(x0),x2),product(i(x0),x0)) = product(product(i(x0),x0),x2),
inference(transitivity,[status(thm)],[119,113,44]) ).
tff(121,plain,
product(t(eta(x0),x1),product(t(eta(x0),x2),product(i(x0),x0))) = product(t(eta(x0),x1),product(product(i(x0),x0),x2)),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
product(t(eta(x0),x1),product(t(eta(x0),x2),product(i(x0),x0))) = product(eta(x0),product(x1,x2)),
inference(transitivity,[status(thm)],[121,111,101,31,29]) ).
tff(123,plain,
quotient(product(t(eta(x0),x1),product(t(eta(x0),x2),product(i(x0),x0))),product(i(x0),x0)) = quotient(product(eta(x0),product(x1,x2)),eta(x0)),
inference(monotonicity,[status(thm)],[122,19]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(product(i(x0),x0),product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2))) = quotient(product(t(eta(x0),x1),product(t(eta(x0),x2),product(i(x0),x0))),product(i(x0),x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
difference(product(i(x0),x0),product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2))) = quotient(product(t(eta(x0),x1),product(t(eta(x0),x2),product(i(x0),x0))),product(i(x0),x0)),
inference(unit_resolution,[status(thm)],[124,58]) ).
tff(126,plain,
difference(product(i(x0),x0),product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2))) = quotient(product(eta(x0),product(x1,x2)),eta(x0)),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
product(product(i(x0),x0),difference(product(i(x0),x0),product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2)))) = product(product(i(x0),x0),quotient(product(eta(x0),product(x1,x2)),eta(x0))),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(i(x0),x0),difference(product(i(x0),x0),product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2)))) = product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
product(product(i(x0),x0),difference(product(i(x0),x0),product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2)))) = product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2)),
inference(unit_resolution,[status(thm)],[128,108]) ).
tff(130,plain,
product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2)) = product(product(i(x0),x0),difference(product(i(x0),x0),product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2)))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
product(eta(x0),t(eta(x0),x1)) = product(product(i(x0),x0),t(eta(x0),x1)),
inference(monotonicity,[status(thm)],[18]) ).
tff(132,plain,
product(product(eta(x0),t(eta(x0),x1)),t(eta(x0),x2)) = product(product(product(i(x0),x0),t(eta(x0),x1)),t(eta(x0),x2)),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
| ( product(eta(x0),product(t(eta(x0),x1),t(eta(x0),x2))) = product(product(eta(x0),t(eta(x0),x1)),t(eta(x0),x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
product(eta(x0),product(t(eta(x0),x1),t(eta(x0),x2))) = product(product(eta(x0),t(eta(x0),x1)),t(eta(x0),x2)),
inference(unit_resolution,[status(thm)],[133,26]) ).
tff(135,plain,
product(product(i(x0),x0),product(t(eta(x0),x1),t(eta(x0),x2))) = product(eta(x0),product(t(eta(x0),x1),t(eta(x0),x2))),
inference(monotonicity,[status(thm)],[19]) ).
tff(136,plain,
product(product(i(x0),x0),product(t(eta(x0),x1),t(eta(x0),x2))) = product(product(i(x0),x0),quotient(product(eta(x0),product(x1,x2)),eta(x0))),
inference(transitivity,[status(thm)],[135,134,132,130,127]) ).
tff(137,plain,
difference(product(i(x0),x0),product(product(i(x0),x0),product(t(eta(x0),x1),t(eta(x0),x2)))) = difference(product(i(x0),x0),product(product(i(x0),x0),quotient(product(eta(x0),product(x1,x2)),eta(x0)))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
difference(product(i(x0),x0),product(product(i(x0),x0),quotient(product(eta(x0),product(x1,x2)),eta(x0)))) = difference(product(i(x0),x0),product(product(i(x0),x0),product(t(eta(x0),x1),t(eta(x0),x2)))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(i(x0),x0),product(product(i(x0),x0),quotient(product(eta(x0),product(x1,x2)),eta(x0)))) = quotient(product(eta(x0),product(x1,x2)),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
difference(product(i(x0),x0),product(product(i(x0),x0),quotient(product(eta(x0),product(x1,x2)),eta(x0)))) = quotient(product(eta(x0),product(x1,x2)),eta(x0)),
inference(unit_resolution,[status(thm)],[139,7]) ).
tff(141,plain,
quotient(product(eta(x0),product(x1,x2)),eta(x0)) = difference(product(i(x0),x0),product(product(i(x0),x0),quotient(product(eta(x0),product(x1,x2)),eta(x0)))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),product(x1,x2)) = quotient(product(eta(x0),product(x1,x2)),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
t(eta(x0),product(x1,x2)) = quotient(product(eta(x0),product(x1,x2)),eta(x0)),
inference(unit_resolution,[status(thm)],[142,81]) ).
tff(144,plain,
t(eta(x0),product(x1,x2)) = product(t(eta(x0),x1),t(eta(x0),x2)),
inference(transitivity,[status(thm)],[143,141,138,9]) ).
tff(145,plain,
( ( t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)) )
<=> ( t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,axiom,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(147,plain,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
$false,
inference(unit_resolution,[status(thm)],[147,144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP768-1 : TPTP v9.0.0. Released v4.1.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Jun 19 17:05:18 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.17/0.49 % SZS status Unsatisfiable
% 0.17/0.49 % SZS output start Proof
% See solution above
% 0.17/0.51 % E exiting
%------------------------------------------------------------------------------