%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP710-10 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:08:31 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.46s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 88 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 117 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 15 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 5 ( 5 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 81 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(x1_type,type,
x1: $i ).
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(unit_type,type,
unit: $i ).
tff(i_type,type,
i: $i > $i ).
tff(x0_type,type,
x0: $i ).
tff(1,plain,
^ [A: $i] :
refl(( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
tff(5,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,x1) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
mult(unit,x1) = x1,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(unit,x1)) = mult(unit,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
mult(unit,mult(unit,x1)) = mult(unit,x1),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [A: $i] :
refl(( ( mult(A,i(A)) = unit )
<=> ( mult(A,i(A)) = unit ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [A: $i] : ( mult(A,i(A)) = unit )
<=> ! [A: $i] : ( mult(A,i(A)) = unit ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [A: $i] : ( mult(A,i(A)) = unit )
<=> ! [A: $i] : ( mult(A,i(A)) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [A: $i] : ( mult(A,i(A)) = unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
tff(16,plain,
! [A: $i] : ( mult(A,i(A)) = unit ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [A: $i] : ( mult(A,i(A)) = unit ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [A: $i] : ( mult(A,i(A)) = unit ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [A: $i] : ( mult(A,i(A)) = unit )
| ( mult(x0,i(x0)) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
mult(x0,i(x0)) = unit,
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
^ [A: $i] :
refl(( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
tff(25,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(x0,unit) = x0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
mult(x0,unit) = x0,
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(x0,unit),unit) = mult(x0,unit) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
mult(mult(x0,unit),unit) = mult(x0,unit),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
mult(mult(mult(x0,unit),unit),unit) = mult(mult(x0,unit),unit),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
mult(mult(mult(x0,unit),unit),unit) = x0,
inference(transitivity,[status(thm)],[32,31,29]) ).
tff(34,plain,
mult(mult(mult(mult(x0,unit),unit),unit),i(x0)) = mult(x0,i(x0)),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
tff(39,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(x0,unit),mult(unit,mult(unit,i(x0)))) = mult(mult(mult(mult(x0,unit),unit),unit),i(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
mult(mult(x0,unit),mult(unit,mult(unit,i(x0)))) = mult(mult(mult(mult(x0,unit),unit),unit),i(x0)),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(unit,i(x0))) = mult(unit,i(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
mult(unit,mult(unit,i(x0))) = mult(unit,i(x0)),
inference(unit_resolution,[status(thm)],[44,7]) ).
tff(46,plain,
mult(unit,i(x0)) = mult(unit,mult(unit,i(x0))),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(x0,unit)) = mult(x0,unit) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
mult(unit,mult(x0,unit)) = mult(x0,unit),
inference(unit_resolution,[status(thm)],[47,7]) ).
tff(49,plain,
mult(mult(x0,unit),i(x0)) = mult(x0,i(x0)),
inference(monotonicity,[status(thm)],[29]) ).
tff(50,plain,
mult(mult(x0,unit),i(x0)) = unit,
inference(transitivity,[status(thm)],[49,20]) ).
tff(51,plain,
mult(mult(x0,unit),mult(mult(x0,unit),i(x0))) = mult(mult(x0,unit),unit),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
mult(mult(x0,unit),mult(mult(x0,unit),i(x0))) = mult(x0,unit),
inference(transitivity,[status(thm)],[51,31]) ).
tff(53,plain,
mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),i(x0)))) = mult(unit,mult(x0,unit)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),i(x0)))) = mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),i(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),i(x0)))) = mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),i(x0)),
inference(unit_resolution,[status(thm)],[54,41]) ).
tff(56,plain,
mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),i(x0)) = mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),i(x0)))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,i(x0)) = i(x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
mult(unit,i(x0)) = i(x0),
inference(unit_resolution,[status(thm)],[57,7]) ).
tff(59,plain,
mult(unit,mult(unit,i(x0))) = i(x0),
inference(transitivity,[status(thm)],[45,58]) ).
tff(60,plain,
mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,mult(unit,i(x0)))) = mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),i(x0)),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,i(x0))) = mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,mult(unit,i(x0)))),
inference(monotonicity,[status(thm)],[46]) ).
tff(62,plain,
mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,i(x0))) = mult(x0,unit),
inference(transitivity,[status(thm)],[61,60,56,53,48]) ).
tff(63,plain,
mult(mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,i(x0))),mult(unit,i(x0))) = mult(mult(x0,unit),mult(unit,mult(unit,i(x0)))),
inference(monotonicity,[status(thm)],[62,46]) ).
tff(64,plain,
mult(mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,i(x0))),mult(unit,i(x0))) = unit,
inference(transitivity,[status(thm)],[63,43,34,20]) ).
tff(65,plain,
mult(mult(mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1)) = mult(unit,mult(unit,x1)),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))) = mult(mult(mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))) = mult(mult(mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1)),
inference(unit_resolution,[status(thm)],[66,41]) ).
tff(68,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))))) = mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))))) = mult(mult(mult(unit,mult(x0,unit)),mult(x0,unit)),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))),
inference(unit_resolution,[status(thm)],[68,41]) ).
tff(70,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))))) = mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))))) = mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1))))),
inference(unit_resolution,[status(thm)],[70,7]) ).
tff(72,plain,
mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1))))) = mult(unit,mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))) = mult(mult(mult(mult(x0,unit),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))) = mult(mult(mult(mult(x0,unit),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1)),
inference(unit_resolution,[status(thm)],[73,41]) ).
tff(75,plain,
mult(mult(mult(mult(x0,unit),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1)) = mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1)))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
x0 = mult(x0,unit),
inference(symmetry,[status(thm)],[29]) ).
tff(77,plain,
mult(x0,mult(mult(mult(mult(x0,unit),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1))) = mult(mult(x0,unit),mult(mult(x0,unit),mult(mult(unit,i(x0)),mult(mult(unit,i(x0)),mult(unit,x1))))),
inference(monotonicity,[status(thm)],[76,75]) ).
tff(78,plain,
mult(x0,mult(mult(mult(mult(x0,unit),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1))) = x1,
inference(transitivity,[status(thm)],[77,72,69,67,65,11,9]) ).
tff(79,plain,
^ [X2: $i] :
refl(( ( mult(x0,X2) != x1 )
<=> ( mult(x0,X2) != x1 ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [X2: $i] : ( mult(x0,X2) != x1 )
<=> ! [X2: $i] : ( mult(x0,X2) != x1 ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [X2: $i] : ( mult(x0,X2) != x1 )
<=> ! [X2: $i] : ( mult(x0,X2) != x1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
! [X2: $i] : ( mult(x0,X2) != x1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(83,plain,
! [X2: $i] : ( mult(x0,X2) != x1 ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [X2: $i] : ( mult(x0,X2) != x1 ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [X2: $i] : ( mult(x0,X2) != x1 ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [X2: $i] : ( mult(x0,X2) != x1 )
| ( mult(x0,mult(mult(mult(mult(x0,unit),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1))) != x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
mult(x0,mult(mult(mult(mult(x0,unit),mult(unit,i(x0))),mult(unit,i(x0))),mult(unit,x1))) != x1,
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
$false,
inference(unit_resolution,[status(thm)],[87,78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP710-10 : TPTP v9.0.0. Released v8.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 16:58:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.22/0.46 % SZS status Unsatisfiable
% 0.22/0.46 % SZS output start Proof
% See solution above
% 0.22/0.47 % E exiting
%------------------------------------------------------------------------------