%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN310-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:43 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 40
% Syntax : Number of formulae : 82 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 296 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 400 ( 190 ~; 184 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 252 ( 240 !; 0 ?; 252 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: ( $i * $i * $i ) > $o ).
tff(g_type,type,
g: $i > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(f_type,type,
f: $i > $i ).
tff(1,plain,
( p(f(g(a)),f(g(b)),f(g(c)))
<=> p(f(g(a)),f(g(b)),f(g(c))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
p(f(g(a)),f(g(b)),f(g(c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
tff(3,plain,
p(f(g(a)),f(g(b)),f(g(c))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i,X2: $i,X1: $i] :
refl(( ( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
<=> ( ~ p(f(X),X1,X2)
| p(X,X1,X2) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
tff(8,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(a)),f(g(b)),f(g(c)))
| p(g(a),f(g(b)),f(g(c))) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(a)),f(g(b)),f(g(c)))
| p(g(a),f(g(b)),f(g(c))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(a)),f(g(b)),f(g(c)))
| p(g(a),f(g(b)),f(g(c))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(a)),f(g(b)),f(g(c)))
| p(g(a),f(g(b)),f(g(c))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
p(g(a),f(g(b)),f(g(c))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [X: $i,X2: $i,X1: $i] :
refl(( ( ~ p(X2,X1,X)
| p(X,X1,X2) )
<=> ( ~ p(X2,X1,X)
| p(X,X1,X2) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
tff(19,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(a),f(g(b)),f(g(c)))
| p(f(g(c)),f(g(b)),g(a)) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(a),f(g(b)),f(g(c)))
| p(f(g(c)),f(g(b)),g(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(a),f(g(b)),f(g(c)))
| p(f(g(c)),f(g(b)),g(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(a),f(g(b)),f(g(c)))
| p(f(g(c)),f(g(b)),g(a)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
p(f(g(c)),f(g(b)),g(a)),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(c)),f(g(b)),g(a))
| p(g(c),f(g(b)),g(a)) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(c)),f(g(b)),g(a))
| p(g(c),f(g(b)),g(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(c)),f(g(b)),g(a))
| p(g(c),f(g(b)),g(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(c)),f(g(b)),g(a))
| p(g(c),f(g(b)),g(a)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
p(g(c),f(g(b)),g(a)),
inference(unit_resolution,[status(thm)],[28,10,25]) ).
tff(30,plain,
^ [X: $i,X2: $i,X1: $i] :
refl(( ( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
<=> ( ~ p(X,X1,g(X2))
| p(X,X1,X2) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
tff(34,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(g(c),f(g(b)),g(a))
| p(g(c),f(g(b)),a) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(g(c),f(g(b)),g(a))
| p(g(c),f(g(b)),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(g(c),f(g(b)),g(a))
| p(g(c),f(g(b)),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(g(c),f(g(b)),g(a))
| p(g(c),f(g(b)),a) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
p(g(c),f(g(b)),a),
inference(unit_resolution,[status(thm)],[39,36,29]) ).
tff(41,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(c),f(g(b)),a)
| p(a,f(g(b)),g(c)) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(c),f(g(b)),a)
| p(a,f(g(b)),g(c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(c),f(g(b)),a)
| p(a,f(g(b)),g(c)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(c),f(g(b)),a)
| p(a,f(g(b)),g(c)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
p(a,f(g(b)),g(c)),
inference(unit_resolution,[status(thm)],[43,21,40]) ).
tff(45,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(a,f(g(b)),g(c))
| p(a,f(g(b)),c) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(a,f(g(b)),g(c))
| p(a,f(g(b)),c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(a,f(g(b)),g(c))
| p(a,f(g(b)),c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(a,f(g(b)),g(c))
| p(a,f(g(b)),c) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
p(a,f(g(b)),c),
inference(unit_resolution,[status(thm)],[47,36,44]) ).
tff(49,plain,
^ [X: $i,X2: $i,X1: $i] :
refl(( ( ~ p(X1,X,X2)
| p(X,X1,X2) )
<=> ( ~ p(X1,X,X2)
| p(X,X1,X2) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
tff(53,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
| ~ p(a,f(g(b)),c)
| p(f(g(b)),a,c) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
| ~ p(a,f(g(b)),c)
| p(f(g(b)),a,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
| ~ p(a,f(g(b)),c)
| p(f(g(b)),a,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
| ~ p(a,f(g(b)),c)
| p(f(g(b)),a,c) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
p(f(g(b)),a,c),
inference(unit_resolution,[status(thm)],[58,55,48]) ).
tff(60,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(b)),a,c)
| p(g(b),a,c) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(b)),a,c)
| p(g(b),a,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(b)),a,c)
| p(g(b),a,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(f(X),X1,X2)
| p(X,X1,X2) )
| ~ p(f(g(b)),a,c)
| p(g(b),a,c) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
p(g(b),a,c),
inference(unit_resolution,[status(thm)],[62,10,59]) ).
tff(64,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(b),a,c)
| p(c,a,g(b)) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(b),a,c)
| p(c,a,g(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(b),a,c)
| p(c,a,g(b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(g(b),a,c)
| p(c,a,g(b)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
p(c,a,g(b)),
inference(unit_resolution,[status(thm)],[66,21,63]) ).
tff(68,plain,
( ~ p(a,b,c)
<=> ~ p(a,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
~ p(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
tff(70,plain,
~ p(a,b,c),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
| ~ p(b,a,c)
| p(a,b,c) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
| ~ p(b,a,c)
| p(a,b,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
| ~ p(b,a,c)
| p(a,b,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X1,X,X2)
| p(X,X1,X2) )
| ~ p(b,a,c)
| p(a,b,c) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
~ p(b,a,c),
inference(unit_resolution,[status(thm)],[73,55,70]) ).
tff(75,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(c,a,b)
| p(b,a,c) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(c,a,b)
| p(b,a,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(c,a,b)
| p(b,a,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X2,X1,X)
| p(X,X1,X2) )
| ~ p(c,a,b)
| p(b,a,c) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
~ p(c,a,b),
inference(unit_resolution,[status(thm)],[77,21,74]) ).
tff(79,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(c,a,g(b))
| p(c,a,b) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(c,a,g(b))
| p(c,a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(c,a,g(b))
| p(c,a,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,g(X2))
| p(X,X1,X2) )
| ~ p(c,a,g(b))
| p(c,a,b) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,36,78,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN310-1 : TPTP v9.0.0. Released v1.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:30:42 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------