%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN365+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:10:11 AM UTC 2026
% Result : Theorem 0.15s 5.41s
% Output : Proof 0.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(x2116,conjecture,
( ( ! [W] :
( big_p(W)
=> ( big_p(h(W))
& big_p(g(W)) ) )
& ! [X] :
? [Y] :
( big_p(X)
=> ( big_p(Y)
& big_r(X,g(h(Y))) ) ) )
=> ! [X] :
( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) ),
file('theBenchmark.p',x2116) ).
fof(f_1_1,negated_conjecture,
( ~ ! [X] :
( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) )
& ! [W] :
( big_p(W)
=> ( big_p(h(W))
& big_p(g(W)) ) )
& ! [X] :
? [Y] :
( big_p(X)
=> ( big_p(Y)
& big_r(X,g(h(Y))) ) ) ),
inference(negate,[status(cth)],[x2116]) ).
fof(f_1_2,negated_conjecture,
( ? [X] :
( ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) )
& big_p(X) )
& ! [W] :
( ( big_p(h(W))
& big_p(g(W)) )
| ~ big_p(W) )
& ! [X] :
? [Y] :
( ( big_p(Y)
& big_r(X,g(h(Y))) )
| ~ big_p(X) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
( ? [U_4] :
( ! [U_3] :
( ~ big_p(U_3)
| ~ big_r(U_4,U_3) )
& big_p(U_4) )
& ! [U_2] :
( ( big_p(h(U_2))
& big_p(g(U_2)) )
| ~ big_p(U_2) )
& ! [U_1] :
? [U_0] :
( ( big_p(U_0)
& big_r(U_1,g(h(U_0))) )
| ~ big_p(U_1) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_4] :
( ! [U_3] :
( ~ big_p(U_3)
| ~ big_r(U_4,U_3) )
& big_p(U_4) )
& ! [U_2] :
( ( big_p(h(U_2))
& big_p(g(U_2)) )
| ~ big_p(U_2) )
& ! [U_1] :
( ? [U_0] :
( big_p(U_0)
& big_r(U_1,g(h(U_0))) )
| ~ big_p(U_1) ) ),
inference(miniscope,[status(thm)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_4] :
( ! [U_3] :
( ~ big_p(U_3)
| ~ big_r(U_4,U_3) )
& big_p(U_4) )
& ! [U_2] :
( ( big_p(h(U_2))
& big_p(g(U_2)) )
| ~ big_p(U_2) )
& ! [U_1] :
( ( big_p(sK1(U_1))
& big_r(U_1,g(h(sK1(U_1)))) )
| ~ big_p(U_1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_1))],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ! [U_3] :
( ~ big_p(U_3)
| ~ big_r(sK2,U_3) )
& big_p(sK2)
& ! [U_2] :
( ( big_p(h(U_2))
& big_p(g(U_2)) )
| ~ big_p(U_2) )
& ! [U_1] :
( ( big_p(sK1(U_1))
& big_r(U_1,g(h(sK1(U_1)))) )
| ~ big_p(U_1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ! [U_2] :
( big_p(h(U_2))
| ~ sP1(U_2) )
& ! [U_2] :
( big_p(g(U_2))
| ~ sP1(U_2) )
& ! [U_1] :
( big_p(sK1(U_1))
| ~ sP0(U_1) )
& ! [U_1] :
( big_r(U_1,g(h(sK1(U_1))))
| ~ sP0(U_1) )
& ! [U_3] :
( ~ big_p(U_3)
| ~ big_r(sK2,U_3) )
& big_p(sK2)
& ! [U_2] :
( sP1(U_2)
| ~ big_p(U_2) )
& ! [U_1] :
( sP0(U_1)
| ~ big_p(U_1) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
( sP0(U_1)
| ~ big_p(U_1) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
( sP1(U_2)
| ~ big_p(U_2) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,negated_conjecture,
big_p(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_11,negated_conjecture,
( ~ big_p(U_3)
| ~ big_r(sK2,U_3) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,negated_conjecture,
( big_r(U_1,g(h(sK1(U_1))))
| ~ sP0(U_1) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_13,negated_conjecture,
( big_p(sK1(U_1))
| ~ sP0(U_1) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,negated_conjecture,
( big_p(g(U_2))
| ~ sP1(U_2) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_15,negated_conjecture,
( big_p(h(U_2))
| ~ sP1(U_2) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN365+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n006.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 06:29:48 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.15/5.41 % SZS status Theorem for theBenchmark
% 0.15/5.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------