%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN631-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 03:35:22 PM UTC 2026
% Result : Unsatisfiable 48.19s 6.54s
% Output : Proof 48.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 40 unt; 0 def)
% Number of atoms : 104 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 46 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 116 ( 3 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f34,negated_conjecture,
( ~ p23(f13(X30,X31),f11(f15(X29)))
| p23(f13(f19(X29,X30,X31),X31),f11(X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_35) ).
fof(f34_nnf,plain,
! [X29,X30,X31] :
( ~ p23(f13(X30,X31),f11(f15(X29)))
| p23(f13(f19(X29,X30,X31),X31),f11(X29)) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X29,X30,X31] :
( ~ p23(f13(X30,X31),f11(f15(X29)))
| p23(f13(f19(X29,X30,X31),X31),f11(X29)) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
( ~ p23(f13(X1,X2),f11(f15(X0)))
| p23(f13(f19(X0,X1,X2),X2),f11(X0)) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi33,negated_conjecture,
ifeq(p23(f13(X0,X1),f11(f15(X2))),true,p23(f13(f19(X2,X0,X1),X1),f11(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(f11,negated_conjecture,
p23(f13(c27,f14(c28)),f11(f15(c24))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_12) ).
fof(f11_nnf,plain,
p23(f13(c27,f14(c28)),f11(f15(c24))),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
p23(f13(c27,f14(c28)),f11(f15(c24))),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,negated_conjecture,
p23(f13(c27,f14(c28)),f11(f15(c24))) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h137,plain,
p23(f13(f19(c24,c27,f14(c28)),f14(c28)),f11(c24)) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi11]) ).
cnf(f33,negated_conjecture,
( ~ p23(f13(X30,X31),f11(f15(X29)))
| p5(X30,f18(f20(c29),f19(X29,X30,X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_34) ).
fof(f33_nnf,plain,
! [X30,X29,X31] :
( ~ p23(f13(X30,X31),f11(f15(X29)))
| p5(X30,f18(f20(c29),f19(X29,X30,X31))) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X30,X29,X31] :
( ~ p23(f13(X30,X31),f11(f15(X29)))
| p5(X30,f18(f20(c29),f19(X29,X30,X31))) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
( ~ p23(f13(X0,X2),f11(f15(X1)))
| p5(X0,f18(f20(c29),f19(X1,X0,X2))) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(hi32,negated_conjecture,
ifeq(p23(f13(X0,X1),f11(f15(X2))),true,p5(X0,f18(f20(c29),f19(X2,X0,X1))),true) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(h42,plain,
p5(c27,f18(f20(c29),f19(c24,c27,f14(c28)))) = true,
inference(hyper_resolution,[status(thm)],[hi32,hi11]) ).
cnf(f24,negated_conjecture,
( ~ p5(X37,X39)
| ~ p5(X37,X38)
| p5(X38,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_25) ).
fof(f24_nnf,plain,
! [X38,X39,X37] :
( ~ p5(X37,X39)
| ~ p5(X37,X38)
| p5(X38,X39) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X38,X39,X37] :
( ~ p5(X37,X39)
| ~ p5(X37,X38)
| p5(X38,X39) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( ~ p5(X2,X1)
| ~ p5(X2,X0)
| p5(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi23,negated_conjecture,
ifeq(p5(X0,X1),true,ifeq(p5(X0,X2),true,p5(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(f4,negated_conjecture,
p5(X37,X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_5) ).
fof(f4_nnf,plain,
! [X37] : p5(X37,X37),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X37] : p5(X37,X37),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
p5(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
p5(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h92,plain,
p5(f18(f20(c29),f19(c24,c27,f14(c28))),c27) = true,
inference(hyper_resolution,[status(thm)],[hi23,h42,hi4]) ).
cnf(f17,negated_conjecture,
( ~ p5(X42,X43)
| p5(f16(X42),f16(X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_18) ).
fof(f17_nnf,plain,
! [X42,X43] :
( ~ p5(X42,X43)
| p5(f16(X42),f16(X43)) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X42,X43] :
( ~ p5(X42,X43)
| p5(f16(X42),f16(X43)) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( ~ p5(X0,X1)
| p5(f16(X0),f16(X1)) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi16,negated_conjecture,
ifeq(p5(X0,X1),true,p5(f16(X0),f16(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h1466,plain,
p5(f16(f18(f20(c29),f19(c24,c27,f14(c28)))),f16(c27)) = true,
inference(hyper_resolution,[status(thm)],[hi16,h92]) ).
cnf(f10,negated_conjecture,
p5(f16(f18(X44,X45)),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_11) ).
fof(f10_nnf,plain,
! [X44,X45] : p5(f16(f18(X44,X45)),X45),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X44,X45] : p5(f16(f18(X44,X45)),X45),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
p5(f16(f18(X0,X1)),X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,negated_conjecture,
p5(f16(f18(X0,X1)),X1) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h7075,plain,
p5(f19(c24,c27,f14(c28)),f16(c27)) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi10,h1466]) ).
cnf(f31,negated_conjecture,
( ~ p5(X9,X11)
| ~ p5(X8,X10)
| p12(f13(X8,X9),f13(X10,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_32) ).
fof(f31_nnf,plain,
! [X8,X9,X10,X11] :
( ~ p5(X9,X11)
| ~ p5(X8,X10)
| p12(f13(X8,X9),f13(X10,X11)) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X8,X9,X10,X11] :
( ~ p5(X9,X11)
| ~ p5(X8,X10)
| p12(f13(X8,X9),f13(X10,X11)) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
( ~ p5(X1,X3)
| ~ p5(X0,X2)
| p12(f13(X0,X1),f13(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(hi30,negated_conjecture,
ifeq(p5(X0,X1),true,ifeq(p5(X2,X3),true,p12(f13(X0,X2),f13(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h7104,plain,
p12(f13(f19(c24,c27,f14(c28)),V0),f13(f16(c27),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi30,h7075,hi4]) ).
cnf(f28,negated_conjecture,
( ~ p10(X27,X26)
| ~ p23(X28,X27)
| ~ p12(X28,X25)
| p23(X25,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_29) ).
fof(f28_nnf,plain,
! [X25,X26,X28,X27] :
( ~ p10(X27,X26)
| ~ p23(X28,X27)
| ~ p12(X28,X25)
| p23(X25,X26) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X25,X26,X28,X27] :
( ~ p10(X27,X26)
| ~ p23(X28,X27)
| ~ p12(X28,X25)
| p23(X25,X26) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( ~ p10(X3,X1)
| ~ p23(X2,X3)
| ~ p12(X2,X0)
| p23(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi27,negated_conjecture,
ifeq(p12(X0,X1),true,ifeq(p23(X0,X2),true,ifeq(p10(X2,X3),true,p23(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f0,negated_conjecture,
p10(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_1) ).
fof(f0_nnf,plain,
! [X0] : p10(X0,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0] : p10(X0,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
p10(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
p10(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
p23(f13(f16(c27),f14(c28)),f11(c24)) = true,
inference(hyper_resolution,[status(thm)],[hi27,h7104,h137,hi0]) ).
cnf(t474,plain,
p23(f13(f16(c27),f14(c28)),f11(c24)) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f12,negated_conjecture,
~ p23(f13(f16(c27),f14(c28)),f11(c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p23_13) ).
fof(f12_nnf,plain,
~ p23(f13(f16(c27),f14(c28)),f11(c24)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ p23(f13(f16(c27),f14(c28)),f11(c24)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ p23(f13(f16(c27),f14(c28)),f11(c24)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
p23(f13(f16(c27),f14(c28)),f11(c24)) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t474]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN631-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n004.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 01:56:25 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 48.19/6.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.19/6.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------