%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN630-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 5.97s 1.24s
% Output : Proof 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 26 unt; 0 def)
% Number of atoms : 46 ( 9 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-4 aty)
% Number of variables : 37 ( 8 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f33,negated_conjecture,
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_34) ).
fof(f33_nnf,plain,
! [X19,X20,X21,X18,X23,X22,X24] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X19,X20,X21,X18,X23,X22,X24] :
( ~ p3(X18,f13(f15(f17(f16(f9(f11(c29)))),X22),f13(f15(f16(f9(f10(f11(c29)))),X24),f14(f16(X23),f15(f16(f9(f10(f11(c29)))),X21)))))
| ~ p22(f12(f9(f10(f11(c29))),f18(X20,f9(f11(c29)))),X23)
| ~ p21(X23,f12(f9(f10(f11(c29))),X20))
| ~ p21(X22,f9(f10(f11(c29))))
| p4(f5(f7(X19,f8(X20,X21)),X18),X23) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
( ~ p3(X3,f13(f15(f17(f16(f9(f11(c29)))),X5),f13(f15(f16(f9(f10(f11(c29)))),X6),f14(f16(X4),f15(f16(f9(f10(f11(c29)))),X2)))))
| ~ p22(f12(f9(f10(f11(c29))),f18(X1,f9(f11(c29)))),X4)
| ~ p21(X4,f12(f9(f10(f11(c29))),X1))
| ~ p21(X5,f9(f10(f11(c29))))
| p4(f5(f7(X0,f8(X1,X2)),X3),X4) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(hi32,negated_conjecture,
ifeq(p21(X0,f9(f10(f11(c29)))),true,ifeq(p21(X1,f12(f9(f10(f11(c29))),X2)),true,ifeq(p22(f12(f9(f10(f11(c29))),f18(X2,f9(f11(c29)))),X1),true,ifeq(p3(X3,f13(f15(f17(f16(f9(f11(c29)))),X0),f13(f15(f16(f9(f10(f11(c29)))),X4),f14(f16(X1),f15(f16(f9(f10(f11(c29)))),X5))))),true,p4(f5(f7(X6,f8(X2,X5)),X3),X1),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(f4,negated_conjecture,
p21(c28,f9(f10(f11(c29)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_5) ).
fof(f4_nnf,plain,
p21(c28,f9(f10(f11(c29)))),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p21(c28,f9(f10(f11(c29)))),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
p21(c28,f9(f10(f11(c29)))) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f5,negated_conjecture,
p21(c27,f12(f9(f10(f11(c29))),c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_6) ).
fof(f5_nnf,plain,
p21(c27,f12(f9(f10(f11(c29))),c24)),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
p21(c27,f12(f9(f10(f11(c29))),c24)),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
p21(c27,f12(f9(f10(f11(c29))),c24)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f16,negated_conjecture,
p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_17) ).
fof(f16_nnf,plain,
p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi15,negated_conjecture,
p22(f12(f9(f10(f11(c29))),f18(c24,f9(f11(c29)))),c27) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f29,negated_conjecture,
p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_30) ).
fof(f29_nnf,plain,
p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25))))),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25))))),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(hi28,negated_conjecture,
p3(c26,f13(f15(f17(f16(f9(f11(c29)))),c28),f13(f15(f16(f9(f10(f11(c29)))),c30),f14(f16(c27),f15(f16(f9(f10(f11(c29)))),c25))))) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t27,plain,
p4(f5(f7(X1,f8(c24,c25)),c26),c27) = true,
inference(hyper_resolution,[status(thm)],[hi32,hi4,hi5,hi15,hi28]) ).
cnf(t150,plain,
p4(f5(f7(X1,f8(c24,c25)),c26),c27) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(f11,negated_conjecture,
~ p4(f5(f7(c23,f8(c24,c25)),c26),c27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p4_12) ).
fof(f11_nnf,plain,
~ p4(f5(f7(c23,f8(c24,c25)),c26),c27),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ p4(f5(f7(c23,f8(c24,c25)),c26),c27),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ p4(f5(f7(c23,f8(c24,c25)),c26),c27),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
p4(f5(f7(c23,f8(c24,c25)),c26),c27) != true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t150]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN630-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 01:57:38 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.97/1.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.97/1.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------