%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN655-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 03:35:25 PM UTC 2026
% Result : Unsatisfiable 12.80s 2.14s
% Output : Proof 12.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 38 unt; 0 def)
% Number of atoms : 74 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 33 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-8 aty)
% Number of variables : 199 ( 53 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f34,negated_conjecture,
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p9(X43,f15(X37,X38,X39,X40,X41,X36,X42,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_35) ).
fof(f34_nnf,plain,
! [X43,X37,X38,X39,X40,X41,X36,X42] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p9(X43,f15(X37,X38,X39,X40,X41,X36,X42,X43)) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X43,X37,X38,X39,X40,X41,X36,X42] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p9(X43,f15(X37,X38,X39,X40,X41,X36,X42,X43)) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
( ~ p21(f11(X2,X3,X6,X7,X0,X4),X5)
| p9(X0,f15(X1,X2,X3,X4,X5,X6,X7,X0)) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi32,negated_conjecture,
ifeq(p21(f11(X0,X1,X2,X3,X4,X5),X6),true,p9(X4,f15(X7,X0,X1,X5,X6,X2,X3,X4)),true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(f26,negated_conjecture,
p21(f11(c24,c25,c26,c27,c22,c28),f11(c29,c30,c31,c32,c23,c33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_27) ).
fof(f26_nnf,plain,
p21(f11(c24,c25,c26,c27,c22,c28),f11(c29,c30,c31,c32,c23,c33)),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
p21(f11(c24,c25,c26,c27,c22,c28),f11(c29,c30,c31,c32,c23,c33)),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi24,negated_conjecture,
p21(f11(c24,c25,c26,c27,c22,c28),f11(c29,c30,c31,c32,c23,c33)) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h2,plain,
p9(c22,f15(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22)) = true,
inference(hyper_resolution,[status(thm)],[hi32,hi24]) ).
cnf(f16,negated_conjecture,
( ~ p9(X177,X179)
| ~ p9(X177,X178)
| p9(X178,X179) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_17) ).
fof(f16_nnf,plain,
! [X178,X179,X177] :
( ~ p9(X177,X179)
| ~ p9(X177,X178)
| p9(X178,X179) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X178,X179,X177] :
( ~ p9(X177,X179)
| ~ p9(X177,X178)
| p9(X178,X179) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ p9(X2,X1)
| ~ p9(X2,X0)
| p9(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi15,negated_conjecture,
ifeq(p9(X0,X1),true,ifeq(p9(X0,X2),true,p9(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f1,negated_conjecture,
p9(X177,X177),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_2) ).
fof(f1_nnf,plain,
! [X177] : p9(X177,X177),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X177] : p9(X177,X177),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p9(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
p9(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h4,plain,
p9(f15(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22),c22) = true,
inference(hyper_resolution,[status(thm)],[hi15,h2,hi1]) ).
cnf(f47,negated_conjecture,
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_48) ).
fof(f47_nnf,plain,
! [X41,X37,X38,X39,X40,X36,X42,X43] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [X41,X37,X38,X39,X40,X36,X42,X43] :
( ~ p21(f11(X38,X39,X36,X42,X43,X40),X41)
| p3(X41,f11(f19(X37,X38,X39,X40,X41,X36,X42,X43),f18(X37,X38,X39,X40,X41,X36,X42,X43),f17(X37,X38,X39,X40,X41,X36,X42,X43),f16(X37,X38,X39,X40,X41,X36,X42,X43),f15(X37,X38,X39,X40,X41,X36,X42,X43),f14(X37,X38,X39,X40,X41,X36,X42,X43))) ),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c47,plain,
( ~ p21(f11(X2,X3,X5,X6,X7,X4),X0)
| p3(X0,f11(f19(X1,X2,X3,X4,X0,X5,X6,X7),f18(X1,X2,X3,X4,X0,X5,X6,X7),f17(X1,X2,X3,X4,X0,X5,X6,X7),f16(X1,X2,X3,X4,X0,X5,X6,X7),f15(X1,X2,X3,X4,X0,X5,X6,X7),f14(X1,X2,X3,X4,X0,X5,X6,X7))) ),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(hi45,negated_conjecture,
ifeq(p21(f11(X0,X1,X2,X3,X4,X5),X6),true,p3(X6,f11(f19(X7,X0,X1,X5,X6,X2,X3,X4),f18(X7,X0,X1,X5,X6,X2,X3,X4),f17(X7,X0,X1,X5,X6,X2,X3,X4),f16(X7,X0,X1,X5,X6,X2,X3,X4),f15(X7,X0,X1,X5,X6,X2,X3,X4),f14(X7,X0,X1,X5,X6,X2,X3,X4))),true) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(h10,plain,
p3(f11(c29,c30,c31,c32,c23,c33),f11(f19(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22),f18(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22),f17(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22),f16(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22),f15(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22),f14(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22))) = true,
inference(hyper_resolution,[status(thm)],[hi45,hi24]) ).
cnf(f29,negated_conjecture,
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p9(X9,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_30) ).
fof(f29_nnf,plain,
! [X9,X14,X5,X6,X7,X8,X3,X10,X11,X12,X13,X4] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p9(X9,X14) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X9,X14,X5,X6,X7,X8,X3,X10,X11,X12,X13,X4] :
( ~ p3(f11(X5,X6,X7,X8,X9,X3),f11(X10,X11,X12,X13,X14,X4))
| p9(X9,X14) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ p3(f11(X2,X3,X4,X5,X0,X6),f11(X7,X8,X9,X10,X1,X11))
| p9(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(hi27,negated_conjecture,
ifeq(p3(f11(X0,X1,X2,X3,X4,X5),f11(X6,X7,X8,X9,X10,X11)),true,p9(X4,X10),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(h25,plain,
p9(c23,f15(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22)) = true,
inference(hyper_resolution,[status(thm)],[hi27,h10]) ).
cnf(h57,plain,
p9(f15(V0,c24,c25,c28,f11(c29,c30,c31,c32,c23,c33),c26,c27,c22),c23) = true,
inference(hyper_resolution,[status(thm)],[hi15,h25,hi1]) ).
cnf(t13,plain,
p9(c23,c22) = true,
inference(hyper_resolution,[status(thm)],[hi15,h57,h4]) ).
cnf(t3052,plain,
p9(c23,c22) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t12,plain,
p9(c22,c23) = true,
inference(hyper_resolution,[status(thm)],[hi15,h4,h57]) ).
cnf(t3136,plain,
p9(c22,c23) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(f9,negated_conjecture,
~ p9(c22,c23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p9_10) ).
fof(f9_nnf,plain,
~ p9(c22,c23),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ p9(c22,c23),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ p9(c22,c23),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f24,negated_conjecture,
~ p3(f11(X196,X197,X198,X199,X200,X201),f4(X202)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p3_25) ).
fof(f24_nnf,plain,
! [X196,X197,X198,X199,X200,X201,X202] : ~ p3(f11(X196,X197,X198,X199,X200,X201),f4(X202)),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X196,X197,X198,X199,X200,X201,X202] : ~ p3(f11(X196,X197,X198,X199,X200,X201),f4(X202)),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
~ p3(f11(X0,X1,X2,X3,X4,X5),f4(X6)),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c24]) ).
cnf(g0_0,plain,
true != ifeq(p9(c22,c23),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(p9(c22,c23),true,false,p9(c23,c22)),
inference(rw,[status(thm)],[g0_0,t3052]) ).
cnf(g0_2,plain,
true != ifeq(p9(c22,c23),p9(c22,c23),false,p9(c23,c22)),
inference(rw,[status(thm)],[g0_1,t3136]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t256]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN655-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 02:00:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.80/2.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.80/2.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------