%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN055-1 : TPTP v9.0.0. Released v1.0.0.
% 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 05:38:04 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 40
% Syntax : Number of formulae : 94 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 485 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 661 ( 292 ~; 318 |; 0 &)
% ( 51 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 110 ( 100 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_f_type,type,
big_f: $i > $o ).
tff(b_type,type,
b: $i ).
tff(big_p_type,type,
big_p: $i > $o ).
tff(big_q_type,type,
big_q: $i > $o ).
tff(a_type,type,
a: $i ).
tff(big_g_type,type,
big_g: $i > $o ).
tff(big_r_type,type,
big_r: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ( ~ big_p(X)
| ~ big_q(X) )
<=> ( ~ big_p(X)
| ~ big_q(X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [X: $i] :
rewrite(( ( ~ big_q(X)
| ~ big_p(X) )
<=> ( ~ big_p(X)
| ~ big_q(X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( ~ big_q(X)
| ~ big_p(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X: $i] :
( ~ big_q(X)
| ~ big_p(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(7,plain,
! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( big_p(a)
<=> big_p(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
big_p(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(13,plain,
big_p(a),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) )
| ~ big_p(a)
| ~ big_q(a) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) )
| ~ big_p(a)
| ~ big_q(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) )
| ~ big_p(a)
| ~ big_q(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| ~ big_q(X) )
| ~ big_p(a)
| ~ big_q(a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ big_q(a),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [X: $i] :
refl(( ( ~ big_p(X)
| big_p(b)
| big_q(X) )
<=> ( ~ big_p(X)
| big_p(b)
| big_q(X) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ big_p(X)
| big_q(X) )
<=> ( ~ big_p(X)
| big_q(X) ) )),
( ( ~ big_p(X)
| big_q(X)
| big_p(b) )
<=> ( ~ big_p(X)
| big_q(X)
| big_p(b) ) )),
rewrite(( ( ~ big_p(X)
| big_q(X)
| big_p(b) )
<=> ( ~ big_p(X)
| big_p(b)
| big_q(X) ) )),
( ( ~ big_p(X)
| big_q(X)
| big_p(b) )
<=> ( ~ big_p(X)
| big_p(b)
| big_q(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_q(X)
| big_p(b) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X: $i] :
( ~ big_p(X)
| big_q(X)
| big_p(b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(24,plain,
! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
| big_p(b)
| ~ big_p(a)
| big_q(a) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
| big_p(b)
| ~ big_p(a)
| big_q(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ big_p(a)
| big_p(b)
| big_q(a) )
<=> ( big_p(b)
| ~ big_p(a)
| big_q(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
| ~ big_p(a)
| big_p(b)
| big_q(a) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
| big_p(b)
| ~ big_p(a)
| big_q(a) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
| ~ big_p(a)
| big_p(b)
| big_q(a) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
| big_p(b)
| ~ big_p(a)
| big_q(a) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
| ~ big_p(a)
| big_p(b)
| big_q(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| big_p(b)
| big_q(X) )
| big_p(b)
| ~ big_p(a)
| big_q(a) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
big_p(b),
inference(unit_resolution,[status(thm)],[33,13,27,17]) ).
tff(35,plain,
^ [X: $i] :
refl(( ( ~ big_p(X)
| big_f(X) )
<=> ( ~ big_p(X)
| big_f(X) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_f(X) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_f(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [X: $i] :
( ~ big_p(X)
| big_f(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(39,plain,
! [X: $i] :
( ~ big_p(X)
| big_f(X) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X: $i] :
( ~ big_p(X)
| big_f(X) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i] :
( ~ big_p(X)
| big_f(X) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
| big_f(b)
| ~ big_p(b) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
| big_f(b)
| ~ big_p(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ big_p(b)
| big_f(b) )
<=> ( big_f(b)
| ~ big_p(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
| ~ big_p(b)
| big_f(b) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
| big_f(b)
| ~ big_p(b) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
| ~ big_p(b)
| big_f(b) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
| big_f(b)
| ~ big_p(b) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
| ~ big_p(b)
| big_f(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| big_f(X) )
| big_f(b)
| ~ big_p(b) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
big_f(b),
inference(unit_resolution,[status(thm)],[47,41,34]) ).
tff(49,plain,
^ [X: $i] :
refl(( ( ~ big_p(X)
| big_g(X) )
<=> ( ~ big_p(X)
| big_g(X) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_g(X) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_g(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [X: $i] :
( ~ big_p(X)
| big_g(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(53,plain,
! [X: $i] :
( ~ big_p(X)
| big_g(X) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X: $i] :
( ~ big_p(X)
| big_g(X) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] :
( ~ big_p(X)
| big_g(X) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
| big_g(b)
| ~ big_p(b) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
| big_g(b)
| ~ big_p(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( ~ big_p(b)
| big_g(b) )
<=> ( big_g(b)
| ~ big_p(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
| ~ big_p(b)
| big_g(b) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
| big_g(b)
| ~ big_p(b) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
| ~ big_p(b)
| big_g(b) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
| big_g(b)
| ~ big_p(b) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
| ~ big_p(b)
| big_g(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| big_g(X) )
| big_g(b)
| ~ big_p(b) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
big_g(b),
inference(unit_resolution,[status(thm)],[61,55,34]) ).
tff(63,plain,
^ [X: $i] :
refl(( ( ~ big_p(X)
| big_r(b)
| big_q(X) )
<=> ( ~ big_p(X)
| big_r(b)
| big_q(X) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ big_p(X)
| big_q(X) )
<=> ( ~ big_p(X)
| big_q(X) ) )),
( ( ~ big_p(X)
| big_q(X)
| big_r(b) )
<=> ( ~ big_p(X)
| big_q(X)
| big_r(b) ) )),
rewrite(( ( ~ big_p(X)
| big_q(X)
| big_r(b) )
<=> ( ~ big_p(X)
| big_r(b)
| big_q(X) ) )),
( ( ~ big_p(X)
| big_q(X)
| big_r(b) )
<=> ( ~ big_p(X)
| big_r(b)
| big_q(X) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X: $i] :
( ~ big_p(X)
| big_q(X)
| big_r(b) )
<=> ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [X: $i] :
( ~ big_p(X)
| big_q(X)
| big_r(b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(69,plain,
! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
| big_r(b)
| ~ big_p(a)
| big_q(a) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
| big_r(b)
| ~ big_p(a)
| big_q(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ big_p(a)
| big_r(b)
| big_q(a) )
<=> ( big_r(b)
| ~ big_p(a)
| big_q(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
| ~ big_p(a)
| big_r(b)
| big_q(a) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
| big_r(b)
| ~ big_p(a)
| big_q(a) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
| ~ big_p(a)
| big_r(b)
| big_q(a) )
<=> ( ~ ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
| big_r(b)
| ~ big_p(a)
| big_q(a) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
| ~ big_p(a)
| big_r(b)
| big_q(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [X: $i] :
( ~ big_p(X)
| big_r(b)
| big_q(X) )
| big_r(b)
| ~ big_p(a)
| big_q(a) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
big_r(b),
inference(unit_resolution,[status(thm)],[78,13,72,17]) ).
tff(80,plain,
^ [X: $i] :
refl(( ( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) )
<=> ( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) )
<=> ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) )
<=> ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
^ [X: $i] :
rewrite(( ( ~ big_f(X)
| ~ big_g(X)
| ~ big_r(X) )
<=> ( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [X: $i] :
( ~ big_f(X)
| ~ big_g(X)
| ~ big_r(X) )
<=> ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,axiom,
! [X: $i] :
( ~ big_f(X)
| ~ big_g(X)
| ~ big_r(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(86,plain,
! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
( ( ~ ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) )
| ~ big_r(b)
| ~ big_g(b)
| ~ big_f(b) )
<=> ( ~ ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) )
| ~ big_r(b)
| ~ big_g(b)
| ~ big_f(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) )
| ~ big_r(b)
| ~ big_g(b)
| ~ big_f(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [X: $i] :
( ~ big_r(X)
| ~ big_g(X)
| ~ big_f(X) )
| ~ big_r(b)
| ~ big_g(b)
| ~ big_f(b) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ~ big_g(b)
| ~ big_f(b) ),
inference(unit_resolution,[status(thm)],[92,89,79]) ).
tff(94,plain,
$false,
inference(unit_resolution,[status(thm)],[93,62,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN055-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 : Fri Jun 20 12:27:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------