%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN712-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 03:35:32 PM UTC 2026
% Result : Unsatisfiable 6.52s 1.43s
% Output : Proof 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 39 unt; 0 def)
% Number of atoms : 99 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 46 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 43 ( 43 usr; 15 con; 0-4 aty)
% Number of variables : 177 ( 28 sgn 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f81,negated_conjecture,
( ~ p3(X124,X126)
| ~ p2(X123,X125)
| p4(f5(X123,X124),f5(X125,X126)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_82) ).
fof(f81_nnf,plain,
! [X123,X124,X125,X126] :
( ~ p3(X124,X126)
| ~ p2(X123,X125)
| p4(f5(X123,X124),f5(X125,X126)) ),
inference(nnf_transformation,[status(thm)],[f81]) ).
fof(f81_sk,plain,
! [X123,X124,X125,X126] :
( ~ p3(X124,X126)
| ~ p2(X123,X125)
| p4(f5(X123,X124),f5(X125,X126)) ),
inference(skolemisation,[status(esa)],[f81_nnf]) ).
cnf(c81,plain,
( ~ p3(X1,X3)
| ~ p2(X0,X2)
| p4(f5(X0,X1),f5(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f81_sk]) ).
cnf(hi80,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p3(X2,X3),true,p4(f5(X0,X2),f5(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(f27,negated_conjecture,
p2(X44,X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_28) ).
fof(f27_nnf,plain,
! [X44] : p2(X44,X44),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X44] : p2(X44,X44),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi27,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(f103,negated_conjecture,
p3(f16(f19(f21(c70,f8(f11(f13(c65,X24),X25),X26)),X27),X28),f8(f11(f13(c65,f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28)),f43(f45(f47(f49(f51(c75,X24),X25),X26),X27),X28)),f53(f55(f57(f59(f61(c76,X24),X25),X26),X27),X28))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_104) ).
fof(f103_nnf,plain,
! [X24,X25,X26,X27,X28] : p3(f16(f19(f21(c70,f8(f11(f13(c65,X24),X25),X26)),X27),X28),f8(f11(f13(c65,f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28)),f43(f45(f47(f49(f51(c75,X24),X25),X26),X27),X28)),f53(f55(f57(f59(f61(c76,X24),X25),X26),X27),X28))),
inference(nnf_transformation,[status(thm)],[f103]) ).
fof(f103_sk,plain,
! [X24,X25,X26,X27,X28] : p3(f16(f19(f21(c70,f8(f11(f13(c65,X24),X25),X26)),X27),X28),f8(f11(f13(c65,f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28)),f43(f45(f47(f49(f51(c75,X24),X25),X26),X27),X28)),f53(f55(f57(f59(f61(c76,X24),X25),X26),X27),X28))),
inference(skolemisation,[status(esa)],[f103_nnf]) ).
cnf(c103,plain,
p3(f16(f19(f21(c70,f8(f11(f13(c65,X0),X1),X2)),X3),X4),f8(f11(f13(c65,f23(f25(f27(f29(f31(c74,X0),X1),X2),X3),X4)),f43(f45(f47(f49(f51(c75,X0),X1),X2),X3),X4)),f53(f55(f57(f59(f61(c76,X0),X1),X2),X3),X4))),
inference(cnf_transformation,[status(esa)],[f103_sk]) ).
cnf(hi101,negated_conjecture,
p3(f16(f19(f21(c70,f8(f11(f13(c65,X0),X1),X2)),X3),X4),f8(f11(f13(c65,f23(f25(f27(f29(f31(c74,X0),X1),X2),X3),X4)),f43(f45(f47(f49(f51(c75,X0),X1),X2),X3),X4)),f53(f55(f57(f59(f61(c76,X0),X1),X2),X3),X4))) = true,
inference(equality_encoding,[status(esa)],[c103]) ).
cnf(h29,plain,
p4(f5(V0,f16(f19(f21(c70,f8(f11(f13(c65,V1),V2),V3)),V4),V5)),f5(V0,f8(f11(f13(c65,f23(f25(f27(f29(f31(c74,V1),V2),V3),V4),V5)),f43(f45(f47(f49(f51(c75,V1),V2),V3),V4),V5)),f53(f55(f57(f59(f61(c76,V1),V2),V3),V4),V5)))) = true,
inference(hyper_resolution,[status(thm)],[hi80,hi27,hi101]) ).
cnf(f68,negated_conjecture,
( ~ p32(X201,X200)
| ~ p62(X202,X201)
| ~ p4(X202,X199)
| p62(X199,X200) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p62_69) ).
fof(f68_nnf,plain,
! [X199,X200,X202,X201] :
( ~ p32(X201,X200)
| ~ p62(X202,X201)
| ~ p4(X202,X199)
| p62(X199,X200) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [X199,X200,X202,X201] :
( ~ p32(X201,X200)
| ~ p62(X202,X201)
| ~ p4(X202,X199)
| p62(X199,X200) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( ~ p32(X3,X1)
| ~ p62(X2,X3)
| ~ p4(X2,X0)
| p62(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(hi67,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p62(X0,X2),true,ifeq(p32(X2,X3),true,p62(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(f99,negated_conjecture,
p62(f5(c64,f16(f19(f21(c70,f8(f11(f13(c65,c66),c67),c68)),c71),c72)),c69),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p62_100) ).
fof(f99_nnf,plain,
p62(f5(c64,f16(f19(f21(c70,f8(f11(f13(c65,c66),c67),c68)),c71),c72)),c69),
inference(nnf_transformation,[status(thm)],[f99]) ).
cnf(c99,plain,
p62(f5(c64,f16(f19(f21(c70,f8(f11(f13(c65,c66),c67),c68)),c71),c72)),c69),
inference(cnf_transformation,[status(esa)],[f99_nnf]) ).
cnf(hi98,negated_conjecture,
p62(f5(c64,f16(f19(f21(c70,f8(f11(f13(c65,c66),c67),c68)),c71),c72)),c69) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
cnf(f19,negated_conjecture,
p32(X92,X92),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p32_20) ).
fof(f19_nnf,plain,
! [X92] : p32(X92,X92),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X92] : p32(X92,X92),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
p32(X0,X0),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,negated_conjecture,
p32(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h112,plain,
p62(f5(c64,f8(f11(f13(c65,f23(f25(f27(f29(f31(c74,c66),c67),c68),c71),c72)),f43(f45(f47(f49(f51(c75,c66),c67),c68),c71),c72)),f53(f55(f57(f59(f61(c76,c66),c67),c68),c71),c72))),c69) = true,
inference(hyper_resolution,[status(thm)],[hi67,h29,hi98,hi19]) ).
cnf(f96,negated_conjecture,
( ~ p62(f5(c64,f8(f11(f13(c65,X203),X205),X206)),X204)
| p62(X203,X204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p62_97) ).
fof(f96_nnf,plain,
! [X203,X204,X205,X206] :
( ~ p62(f5(c64,f8(f11(f13(c65,X203),X205),X206)),X204)
| p62(X203,X204) ),
inference(nnf_transformation,[status(thm)],[f96]) ).
fof(f96_sk,plain,
! [X203,X204,X205,X206] :
( ~ p62(f5(c64,f8(f11(f13(c65,X203),X205),X206)),X204)
| p62(X203,X204) ),
inference(skolemisation,[status(esa)],[f96_nnf]) ).
cnf(c96,plain,
( ~ p62(f5(c64,f8(f11(f13(c65,X0),X2),X3)),X1)
| p62(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f96_sk]) ).
cnf(hi95,negated_conjecture,
ifeq(p62(f5(c64,f8(f11(f13(c65,X0),X1),X2)),X3),true,p62(X0,X3),true) = true,
inference(equality_encoding,[status(esa)],[c96]) ).
cnf(h463,plain,
p62(f23(f25(f27(f29(f31(c74,c66),c67),c68),c71),c72),c69) = true,
inference(hyper_resolution,[status(thm)],[hi95,h112]) ).
cnf(f98,negated_conjecture,
( ~ p62(f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28),X29)
| p62(X24,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p62_99) ).
fof(f98_nnf,plain,
! [X24,X29,X25,X26,X27,X28] :
( ~ p62(f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28),X29)
| p62(X24,X29) ),
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
! [X24,X29,X25,X26,X27,X28] :
( ~ p62(f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28),X29)
| p62(X24,X29) ),
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c98,plain,
( ~ p62(f23(f25(f27(f29(f31(c74,X0),X2),X3),X4),X5),X1)
| p62(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(hi97,negated_conjecture,
ifeq(p62(f23(f25(f27(f29(f31(c74,X0),X1),X2),X3),X4),X5),true,p62(X0,X5),true) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(h467,plain,
p62(c66,c69) = true,
inference(hyper_resolution,[status(thm)],[hi97,h463]) ).
cnf(f97,negated_conjecture,
( ~ p62(X203,X204)
| p62(f5(c64,f8(f11(f13(c65,X203),X205),X206)),X204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p62_98) ).
fof(f97_nnf,plain,
! [X203,X205,X206,X204] :
( ~ p62(X203,X204)
| p62(f5(c64,f8(f11(f13(c65,X203),X205),X206)),X204) ),
inference(nnf_transformation,[status(thm)],[f97]) ).
fof(f97_sk,plain,
! [X203,X205,X206,X204] :
( ~ p62(X203,X204)
| p62(f5(c64,f8(f11(f13(c65,X203),X205),X206)),X204) ),
inference(skolemisation,[status(esa)],[f97_nnf]) ).
cnf(c97,plain,
( ~ p62(X0,X3)
| p62(f5(c64,f8(f11(f13(c65,X0),X1),X2)),X3) ),
inference(cnf_transformation,[status(esa)],[f97_sk]) ).
cnf(hi96,negated_conjecture,
ifeq(p62(X0,X1),true,p62(f5(c64,f8(f11(f13(c65,X0),X2),X3)),X1),true) = true,
inference(equality_encoding,[status(esa)],[c97]) ).
cnf(h478,plain,
p62(f5(c64,f8(f11(f13(c65,c66),V0),V1)),c69) = true,
inference(hyper_resolution,[status(thm)],[hi96,h467]) ).
cnf(f66,negated_conjecture,
~ p62(f5(c64,f8(f11(f13(c65,c66),c67),c68)),c69),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p62_67) ).
fof(f66_nnf,plain,
~ p62(f5(c64,f8(f11(f13(c65,c66),c67),c68)),c69),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
~ p62(f5(c64,f8(f11(f13(c65,c66),c67),c68)),c69),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
~ p62(f5(c64,f8(f11(f13(c65,c66),c67),c68)),c69),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(hi102,negated_conjecture,
ifeq(p62(f5(c64,f8(f11(f13(c65,c66),c67),c68)),c69),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi102,h478]) ).
cnf(t464,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f100,negated_conjecture,
( ~ p62(f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28),X29)
| ~ p63(f36(f39(f41(c73,X27),X28),f37(X25,X29)),f33(X26,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p63_101) ).
fof(f100_nnf,plain,
! [X27,X28,X25,X29,X26,X24] :
( ~ p62(f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28),X29)
| ~ p63(f36(f39(f41(c73,X27),X28),f37(X25,X29)),f33(X26,X29)) ),
inference(nnf_transformation,[status(thm)],[f100]) ).
fof(f100_sk,plain,
! [X27,X28,X25,X29,X26,X24] :
( ~ p62(f23(f25(f27(f29(f31(c74,X24),X25),X26),X27),X28),X29)
| ~ p63(f36(f39(f41(c73,X27),X28),f37(X25,X29)),f33(X26,X29)) ),
inference(skolemisation,[status(esa)],[f100_nnf]) ).
cnf(c100,plain,
( ~ p62(f23(f25(f27(f29(f31(c74,X5),X2),X4),X0),X1),X3)
| ~ p63(f36(f39(f41(c73,X0),X1),f37(X2,X3)),f33(X4,X3)) ),
inference(cnf_transformation,[status(esa)],[f100_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c66,c100]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t464]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN712-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 02:09:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.52/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.52/1.43 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------