%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEV515+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Fri Jul 25 03:54:29 PM UTC 2025
% Result : Theorem 5.65s 1.07s
% Output : CNFRefutation 5.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 85 ( 1 unt; 0 def)
% Number of atoms : 260 ( 0 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 293 ( 118 ~; 147 |; 25 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 52 ( 2 sgn 12 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nc1,plain,
( ! [A] :
? [B] :
( ( g_true_only(B,A)
& ( g_both(B,B)
| g_true_only(B,B) ) )
| ( g_both(B,A)
& ( g_false_only(B,B)
| g_true_only(B,B) ) )
| ( g_false_only(B,A)
& ( g_false_only(B,B)
| g_both(B,B) ) ) )
| ( ? [A] :
( ? [B] :
( g_both(B,A)
& g_both(B,B) )
& ~ ? [B] :
( ( g_true_only(B,A)
& ( g_both(B,B)
| g_true_only(B,B) ) )
| ( g_both(B,A)
& ( g_false_only(B,B)
| g_true_only(B,B) ) )
| ( g_false_only(B,A)
& ( g_false_only(B,B)
| g_both(B,B) ) ) ) )
& ~ ? [A] :
! [B] :
( ( g_true_only(B,A)
& g_false_only(B,B) )
| ( g_false_only(B,A)
& g_true_only(B,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nc1) ).
fof(nc1_negated,plain,
~ ( ! [A] :
? [B] :
( ( g_true_only(B,A)
& ( g_both(B,B)
| g_true_only(B,B) ) )
| ( g_both(B,A)
& ( g_false_only(B,B)
| g_true_only(B,B) ) )
| ( g_false_only(B,A)
& ( g_false_only(B,B)
| g_both(B,B) ) ) )
| ( ? [A] :
( ? [B] :
( g_both(B,A)
& g_both(B,B) )
& ~ ? [B] :
( ( g_true_only(B,A)
& ( g_both(B,B)
| g_true_only(B,B) ) )
| ( g_both(B,A)
& ( g_false_only(B,B)
| g_true_only(B,B) ) )
| ( g_false_only(B,A)
& ( g_false_only(B,B)
| g_both(B,B) ) ) ) )
& ~ ? [A] :
! [B] :
( ( g_true_only(B,A)
& g_false_only(B,B) )
| ( g_false_only(B,A)
& g_true_only(B,B) ) ) ) ),
inference(negate_conjecture,[status(cth)],[nc1]) ).
cnf(1,plain,
( ~ g_true_only(X0,X0)
| ~ g_true_only(X0,sK1) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l0,plain,
( ~ g_true_only(sK2(sK1),sK2(sK1))
| ~ g_true_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(6,plain,
( ~ g_both(X0,X1)
| ~ g_both(X0,X0)
| g_true_only(sK2(X1),X1)
| sP0(X1)
| sP1(X1)
| sP3(X2) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l2,plain,
( ~ g_both(sK1,sK1)
| ~ g_both(sK1,sK1)
| g_true_only(sK2(sK1),sK1)
| sP0(sK1)
| sP1(sK1)
| sP3(sK1) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(8,plain,
( g_false_only(X0,X0)
| sP2(X0)
| ~ sP3(X0) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l201,plain,
( g_false_only(sK1,sK1)
| sP2(sK1)
| ~ sP3(sK1) ),
inference(instantiation,[status(thm)],[8]) ).
fof(exhaustion_g,plain,
! [X_2,X_1] :
( g_true_only(X_2,X_1)
| g_both(X_2,X_1)
| g_false_only(X_2,X_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exhaustion_g) ).
cnf(25,plain,
( g_true_only(X0,X1)
| g_both(X0,X1)
| g_false_only(X0,X1) ),
inference(cnf,[status(esa)],[exhaustion_g]) ).
cnf(l7,plain,
( g_true_only(sK1,sK1)
| g_both(sK1,sK1)
| g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(4,plain,
( ~ g_false_only(X0,X0)
| ~ g_false_only(X0,sK1) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l228,plain,
( ~ g_false_only(sK1,sK1)
| ~ g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(12,plain,
( g_both(sK2(X0),sK2(X0))
| g_false_only(sK2(X0),sK2(X0))
| ~ sP1(X0) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l222,plain,
( g_both(sK2(sK1),sK2(sK1))
| g_false_only(sK2(sK1),sK2(sK1))
| ~ sP1(sK1) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(10,plain,
( g_true_only(X0,X0)
| ~ sP2(X0) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l230,plain,
( g_true_only(sK1,sK1)
| ~ sP2(sK1) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(5,plain,
( ~ g_both(X0,X0)
| ~ g_false_only(X0,sK1) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l225,plain,
( ~ g_both(sK2(sK1),sK2(sK1))
| ~ g_false_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l274,plain,
( ~ g_true_only(sK1,sK1)
| ~ g_true_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(15,plain,
( g_both(sK2(X0),X0)
| ~ sP0(X0) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l645,plain,
( g_both(sK2(sK1),sK1)
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(7,plain,
( ~ g_both(X0,X1)
| ~ g_both(X0,X0)
| g_true_only(sK2(X1),sK2(X1))
| g_both(sK2(X1),sK2(X1))
| sP0(X1)
| sP1(X1)
| sP3(X2) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l1,plain,
( ~ g_both(sK1,sK1)
| ~ g_both(sK1,sK1)
| g_true_only(sK2(sK1),sK2(sK1))
| g_both(sK2(sK1),sK2(sK1))
| sP0(sK1)
| sP1(sK1)
| sP3(sK1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(13,plain,
( g_false_only(sK2(X0),X0)
| ~ sP1(X0) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l4,plain,
( g_false_only(sK2(sK1),sK1)
| ~ sP1(sK1) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l22,plain,
( g_true_only(sK1,sK1)
| g_both(sK1,sK1)
| g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(l9,plain,
( ~ g_both(sK2(sK1),sK2(sK1))
| ~ g_false_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(14,plain,
( g_true_only(sK2(X0),sK2(X0))
| g_false_only(sK2(X0),sK2(X0))
| ~ sP0(X0) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l8,plain,
( g_true_only(sK2(sK1),sK2(sK1))
| g_false_only(sK2(sK1),sK2(sK1))
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(2,plain,
( ~ g_both(X0,sK1)
| ~ g_false_only(X0,X0) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l223,plain,
( ~ g_both(sK2(sK1),sK1)
| ~ g_false_only(sK2(sK1),sK2(sK1)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l6,plain,
( g_true_only(sK1,sK1)
| g_both(sK1,sK1)
| g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(l35,plain,
( ~ g_both(sK2(sK1),sK1)
| ~ g_false_only(sK2(sK1),sK2(sK1)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(3,plain,
( ~ g_true_only(X0,X0)
| ~ g_both(X0,sK1) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l647,plain,
( ~ g_true_only(sK2(sK1),sK2(sK1))
| ~ g_both(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l233,plain,
( ~ g_false_only(sK1,sK1)
| ~ g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l32,plain,
( ~ g_true_only(sK1,sK1)
| ~ g_true_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[1]) ).
fof(both_g,plain,
! [X_2,X_1] :
( g_both(X_2,X_1)
<=> ( g_true(X_2,X_1)
& g_false(X_2,X_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',both_g) ).
cnf(21,plain,
( ~ g_true(X0,X1)
| ~ g_false(X0,X1)
| g_both(X0,X1) ),
inference(cnf,[status(esa)],[both_g]) ).
cnf(l3,plain,
( ~ g_true(sK1,sK1)
| ~ g_false(sK1,sK1)
| g_both(sK1,sK1) ),
inference(instantiation,[status(thm)],[21]) ).
cnf(l42,plain,
( g_both(sK2(sK1),sK1)
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l227,plain,
( ~ g_false_only(sK1,sK1)
| ~ g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l43,plain,
( ~ g_true_only(sK1,sK1)
| ~ g_true_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l28,plain,
( ~ g_true_only(sK1,sK1)
| ~ g_true_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l244,plain,
( g_false_only(sK2(sK1),sK1)
| ~ sP1(sK1) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l648,plain,
( g_true_only(sK2(sK1),sK2(sK1))
| g_false_only(sK2(sK1),sK2(sK1))
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l707,plain,
( g_false_only(sK1,sK1)
| sP2(sK1)
| ~ sP3(sK1) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l13,plain,
( ~ g_false_only(sK1,sK1)
| ~ g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l708,plain,
( g_true_only(sK1,sK1)
| ~ sP2(sK1) ),
inference(instantiation,[status(thm)],[10]) ).
fof(true_only_g,plain,
! [X_2,X_1] :
( g_true_only(X_2,X_1)
<=> ( g_true(X_2,X_1)
& ~ g_false(X_2,X_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',true_only_g) ).
cnf(16,plain,
( ~ g_true_only(X0,X1)
| g_true(X0,X1) ),
inference(cnf,[status(esa)],[true_only_g]) ).
cnf(l12,plain,
( ~ g_true_only(sK1,sK1)
| g_true(sK1,sK1) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l759,plain,
( ~ g_true_only(sK1,sK1)
| ~ g_true_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l157,plain,
( g_both(sK2(sK1),sK2(sK1))
| g_false_only(sK2(sK1),sK2(sK1))
| ~ sP1(sK1) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l353,plain,
( g_true_only(sK2(sK1),sK1)
| g_both(sK2(sK1),sK1)
| g_false_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(l699,plain,
( ~ g_both(sK2(sK1),sK1)
| ~ g_false_only(sK2(sK1),sK2(sK1)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l15,plain,
( g_true_only(sK1,sK1)
| g_both(sK1,sK1)
| g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(l721,plain,
( ~ g_false_only(sK1,sK1)
| ~ g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l361,plain,
( ~ g_false_only(sK2(sK1),sK2(sK1))
| ~ g_false_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l173,plain,
( ~ g_false_only(sK2(sK1),sK2(sK1))
| ~ g_false_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l29,plain,
( ~ g_false_only(sK1,sK1)
| ~ g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l10,plain,
( ~ g_both(sK2(sK1),sK1)
| ~ g_both(sK2(sK1),sK2(sK1))
| g_true_only(sK2(sK1),sK1)
| sP0(sK1)
| sP1(sK1)
| sP3(sK2(sK1)) ),
inference(instantiation,[status(thm)],[6]) ).
fof(false_only_g,plain,
! [X_2,X_1] :
( g_false_only(X_2,X_1)
<=> ( g_false(X_2,X_1)
& ~ g_true(X_2,X_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_only_g) ).
cnf(22,plain,
( ~ g_false_only(X0,X1)
| g_false(X0,X1) ),
inference(cnf,[status(esa)],[false_only_g]) ).
cnf(l5,plain,
( ~ g_false_only(sK1,sK1)
| g_false(sK1,sK1) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(l715,plain,
( g_both(sK2(sK1),sK1)
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l718,plain,
( g_false_only(sK2(sK1),sK2(sK1))
| sP2(sK2(sK1))
| ~ sP3(sK2(sK1)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l11,plain,
( g_true_only(sK2(sK1),sK1)
| g_both(sK2(sK1),sK1)
| g_false_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(l17,plain,
( g_true_only(sK1,sK1)
| g_both(sK1,sK1)
| g_false_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(l80,plain,
( ~ g_true_only(sK1,sK1)
| ~ g_true_only(sK1,sK1) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l717,plain,
( ~ g_both(sK2(sK1),sK1)
| ~ g_false_only(sK2(sK1),sK2(sK1)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l719,plain,
( g_true_only(sK2(sK1),sK2(sK1))
| ~ sP2(sK2(sK1)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(0,plain,
( ~ g_true_only(X0,sK1)
| ~ g_both(X0,X0) ),
inference(cnf,[status(esa)],[nc1_negated]) ).
cnf(l711,plain,
( ~ g_true_only(sK2(sK1),sK1)
| ~ g_both(sK2(sK1),sK2(sK1)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l824,plain,
( ~ g_both(sK2(sK1),sK2(sK1))
| ~ g_false_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l710,plain,
( g_false_only(sK2(sK1),sK1)
| ~ sP1(sK1) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l116,plain,
( ~ g_true_only(sK2(sK1),sK1)
| ~ g_both(sK2(sK1),sK2(sK1)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l720,plain,
( g_true_only(sK2(sK1),sK2(sK1))
| g_false_only(sK2(sK1),sK2(sK1))
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l712,plain,
( ~ g_both(sK2(sK1),sK2(sK1))
| ~ g_false_only(sK2(sK1),sK1) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(23,plain,
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf,[status(esa)],[false_only_g]) ).
cnf(l722,plain,
( ~ g_false_only(sK2(sK1),sK2(sK1))
| ~ g_true(sK2(sK1),sK2(sK1)) ),
inference(instantiation,[status(thm)],[23]) ).
cnf(19,plain,
( ~ g_both(X0,X1)
| g_true(X0,X1) ),
inference(cnf,[status(esa)],[both_g]) ).
cnf(l835,plain,
( ~ g_both(sK2(sK1),sK2(sK1))
| g_true(sK2(sK1),sK2(sK1)) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l201,l7,l228,l222,l230,l225,l274,l645,l1,l4,l22,l9,l8,l223,l6,l35,l647,l233,l32,l3,l42,l227,l43,l28,l244,l648,l707,l13,l708,l12,l759,l157,l353,l699,l15,l721,l361,l173,l29,l10,l5,l715,l718,l11,l17,l80,l717,l719,l711,l824,l710,l116,l720,l712,l722,l835]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV515+1 : TPTP v9.0.0. Released v7.0.0.
% 0.04/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n017.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 : Tue Jul 22 03:35:49 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.36 % launching worker at depth: 10
% 0.20/0.40 % launching worker at depth: 11
% 2.70/0.67 % launching worker at depth: 12
% 5.65/1.07 % SZS status Theorem for theBenchmark
% 5.65/1.07 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------