%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN643-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 : Fri Sep 25 03:35:23 PM UTC 2026
% Result : Unsatisfiable 4.93s 1.11s
% Output : Proof 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 42 unt; 0 def)
% Number of atoms : 78 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,negated_conjecture,
p4(f5(f3(c19)),f5(c19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_11) ).
fof(f10_nnf,plain,
p4(f5(f3(c19)),f5(c19)),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
p4(f5(f3(c19)),f5(c19)),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,negated_conjecture,
p4(f5(f3(c19)),f5(c19)) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h3,plain,
p4(f5(f3(c19)),f5(c19)) = true,
inference(hyper_resolution,[status(thm)],[hi10]) ).
cnf(f9,negated_conjecture,
p4(f5(f3(c18)),f5(c18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_10) ).
fof(f9_nnf,plain,
p4(f5(f3(c18)),f5(c18)),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
p4(f5(f3(c18)),f5(c18)),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi9,negated_conjecture,
p4(f5(f3(c18)),f5(c18)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h2,plain,
p4(f5(f3(c18)),f5(c18)) = true,
inference(hyper_resolution,[status(thm)],[hi9]) ).
cnf(f34,negated_conjecture,
( ~ p4(X41,X43)
| ~ p4(X42,X44)
| p4(f9(X41,X42),f9(X43,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_35) ).
fof(f34_nnf,plain,
! [X41,X42,X43,X44] :
( ~ p4(X41,X43)
| ~ p4(X42,X44)
| p4(f9(X41,X42),f9(X43,X44)) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X41,X42,X43,X44] :
( ~ p4(X41,X43)
| ~ p4(X42,X44)
| p4(f9(X41,X42),f9(X43,X44)) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
( ~ p4(X0,X2)
| ~ p4(X1,X3)
| p4(f9(X0,X1),f9(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi33,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X2,X3),true,p4(f9(X2,X0),f9(X3,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(h5,plain,
p4(f9(f5(f3(c19)),f5(f3(c18))),f9(f5(c19),f5(c18))) = true,
inference(hyper_resolution,[status(thm)],[hi33,h2,h3]) ).
cnf(f4,negated_conjecture,
p4(X36,X36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_5) ).
fof(f4_nnf,plain,
! [X36] : p4(X36,X36),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X36] : p4(X36,X36),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
p4(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
p4(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h4,plain,
p4(f9(f5(f3(c19)),f5(f3(c18))),f9(f5(f3(c19)),f5(f3(c18)))) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi4,hi4]) ).
cnf(f23,negated_conjecture,
( ~ p4(X36,X38)
| ~ p4(X36,X37)
| p4(X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_24) ).
fof(f23_nnf,plain,
! [X37,X38,X36] :
( ~ p4(X36,X38)
| ~ p4(X36,X37)
| p4(X37,X38) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X37,X38,X36] :
( ~ p4(X36,X38)
| ~ p4(X36,X37)
| p4(X37,X38) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ p4(X2,X1)
| ~ p4(X2,X0)
| p4(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi23,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X0,X2),true,p4(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h6,plain,
p4(f9(f5(f3(c19)),f5(f3(c18))),f9(f5(c19),f5(c18))) = true,
inference(hyper_resolution,[status(thm)],[hi23,h4,h5]) ).
cnf(f1,negated_conjecture,
p15(f3(c18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3_is_p15_2) ).
fof(f1_nnf,plain,
p15(f3(c18)),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
p15(f3(c18)),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,negated_conjecture,
p15(f3(c18)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h1,plain,
p15(f3(c18)) = true,
inference(hyper_resolution,[status(thm)],[hi1]) ).
cnf(f0,negated_conjecture,
p15(f3(c19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3_is_p15_1) ).
fof(f0_nnf,plain,
p15(f3(c19)),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
p15(f3(c19)),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,negated_conjecture,
p15(f3(c19)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
p15(f3(c19)) = true,
inference(hyper_resolution,[status(thm)],[hi0]) ).
cnf(f36,negated_conjecture,
( ~ p15(X15)
| ~ p15(X14)
| p4(f5(f10(X14,X15)),f9(f5(X14),f5(X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_37) ).
fof(f36_nnf,plain,
! [X14,X15] :
( ~ p15(X15)
| ~ p15(X14)
| p4(f5(f10(X14,X15)),f9(f5(X14),f5(X15))) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [X14,X15] :
( ~ p15(X15)
| ~ p15(X14)
| p4(f5(f10(X14,X15)),f9(f5(X14),f5(X15))) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
( ~ p15(X1)
| ~ p15(X0)
| p4(f5(f10(X0,X1)),f9(f5(X0),f5(X1))) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi35,negated_conjecture,
ifeq(p15(X0),true,ifeq(p15(X1),true,p4(f5(f10(X0,X1)),f9(f5(X0),f5(X1))),true),true) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(h7,plain,
p4(f5(f10(f3(c19),f3(c18))),f9(f5(f3(c19)),f5(f3(c18)))) = true,
inference(hyper_resolution,[status(thm)],[hi35,h0,h1]) ).
cnf(h8,plain,
p4(f9(f5(f3(c19)),f5(f3(c18))),f5(f10(f3(c19),f3(c18)))) = true,
inference(hyper_resolution,[status(thm)],[hi23,h7,hi4]) ).
cnf(t25,plain,
p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))) = true,
inference(hyper_resolution,[status(thm)],[hi23,h8,h6]) ).
cnf(t177,plain,
p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(f27,negated_conjecture,
~ p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p4_28) ).
fof(f27_nnf,plain,
~ p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
~ p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
~ p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(goal_0,negated_conjecture,
p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))) != true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t177]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN643-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 02:01:11 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.93/1.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.93/1.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------