%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP730-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:08:34 AM UTC 2025
% Result : Unsatisfiable 209.32s 209.62s
% Output : Proof 209.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of formulae : 85 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 122 ( 114 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 42 ( 12 ~; 8 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 7 ( 7 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; 5 con; 0-3 aty)
% Number of variables : 162 ( 146 !; 0 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
tff(unit_type,type,
unit: $i ).
tff(asoc_type,type,
asoc: ( $i * $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(c_type,type,
c: $i ).
tff(op_k_type,type,
op_k: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(i_type,type,
i: $i > $i ).
tff(1,plain,
^ [B: $i,D: $i,A: $i,E: $i,C: $i] :
refl(( ( asoc(asoc(A,B,C),D,E) = unit )
<=> ( asoc(asoc(A,B,C),D,E) = unit ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c21) ).
tff(5,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit )
| ( asoc(asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),c,d) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
asoc(asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),c,d) = unit,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
tff(14,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) = asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
mult(unit,asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) = asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [B: $i,A: $i] :
refl(( ( mult(i(A),mult(A,B)) = B )
<=> ( mult(i(A),mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
tff(23,plain,
! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(a),mult(a,b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
mult(i(a),mult(a,b)) = b,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
<=> ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
<=> ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
<=> ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
tff(32,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
| ( mult(a,b) = mult(mult(b,a),op_k(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
mult(a,b) = mult(mult(b,a),op_k(a,b)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
mult(mult(b,a),op_k(a,b)) = mult(a,b),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
mult(i(a),mult(mult(b,a),op_k(a,b))) = mult(i(a),mult(a,b)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
mult(i(a),mult(mult(b,a),op_k(a,b))) = b,
inference(transitivity,[status(thm)],[38,27]) ).
tff(40,plain,
mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))) = mult(i(b),b),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
mult(i(b),b) = mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [A: $i] :
refl(( ( mult(i(A),A) = unit )
<=> ( mult(i(A),A) = unit ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [A: $i] : ( mult(i(A),A) = unit )
<=> ! [A: $i] : ( mult(i(A),A) = unit ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [A: $i] : ( mult(i(A),A) = unit )
<=> ! [A: $i] : ( mult(i(A),A) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [A: $i] : ( mult(i(A),A) = unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
tff(46,plain,
! [A: $i] : ( mult(i(A),A) = unit ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [A: $i] : ( mult(i(A),A) = unit ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [A: $i] : ( mult(i(A),A) = unit ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [A: $i] : ( mult(i(A),A) = unit )
| ( mult(i(b),b) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
mult(i(b),b) = unit,
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
unit = mult(i(b),b),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
unit = mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),
inference(transitivity,[status(thm)],[51,41]) ).
tff(53,plain,
mult(unit,asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) = mult(mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
mult(mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) = mult(unit,asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
<=> ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
tff(59,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
| ( mult(mult(i(b),i(a)),mult(mult(b,a),op_k(a,b))) = mult(mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
mult(mult(i(b),i(a)),mult(mult(b,a),op_k(a,b))) = mult(mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
^ [B: $i,A: $i] :
refl(( ( i(mult(A,B)) = mult(i(A),i(B)) )
<=> ( i(mult(A,B)) = mult(i(A),i(B)) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
<=> ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
<=> ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
tff(68,plain,
! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
| ( i(mult(b,a)) = mult(i(b),i(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
i(mult(b,a)) = mult(i(b),i(a)),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
mult(i(b),i(a)) = i(mult(b,a)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
mult(mult(i(b),i(a)),mult(mult(b,a),op_k(a,b))) = mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))) = mult(mult(i(b),i(a)),mult(mult(b,a),op_k(a,b))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))) = op_k(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))) = op_k(a,b),
inference(unit_resolution,[status(thm)],[76,25]) ).
tff(78,plain,
op_k(a,b) = mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
op_k(a,b) = asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),
inference(transitivity,[status(thm)],[78,75,63,54,18]) ).
tff(80,plain,
asoc(op_k(a,b),c,d) = asoc(asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),c,d),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
asoc(op_k(a,b),c,d) = unit,
inference(transitivity,[status(thm)],[80,9]) ).
tff(82,plain,
( ( asoc(op_k(a,b),c,d) != unit )
<=> ( asoc(op_k(a,b),c,d) != unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
asoc(op_k(a,b),c,d) != unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(84,plain,
asoc(op_k(a,b),c,d) != unit,
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
$false,
inference(unit_resolution,[status(thm)],[84,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP730-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 17:01:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 209.32/209.62 % SZS status Unsatisfiable
% 209.32/209.62 % SZS output start Proof
% See solution above
% 209.32/209.64 % E exiting
%------------------------------------------------------------------------------