%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN632-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 5.89s 6.44s
% Output : Proof 5.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 34 unt; 0 def)
% Number of atoms : 114 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 102 ( 54 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-4 aty)
% Number of variables : 143 ( 7 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f33,negated_conjecture,
( ~ p3(X43,X44)
| p21(f5(f7(f10(c24,f12(c25,c26)),X42),X43),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_34) ).
fof(f33_nnf,plain,
! [X42,X43,X44] :
( ~ p3(X43,X44)
| p21(f5(f7(f10(c24,f12(c25,c26)),X42),X43),X44) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X42,X43,X44] :
( ~ p3(X43,X44)
| p21(f5(f7(f10(c24,f12(c25,c26)),X42),X43),X44) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
( ~ p3(X1,X2)
| p21(f5(f7(f10(c24,f12(c25,c26)),X0),X1),X2) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(hi33,negated_conjecture,
ifeq(p3(X0,X1),true,p21(f5(f7(f10(c24,f12(c25,c26)),X2),X0),X1),true) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(f5,negated_conjecture,
p3(X46,X46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_6) ).
fof(f5_nnf,plain,
! [X46] : p3(X46,X46),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X46] : p3(X46,X46),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
p3(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,negated_conjecture,
p3(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
p21(f5(f7(f10(c24,f12(c25,c26)),V0),V1),V1) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi5]) ).
cnf(f35,negated_conjecture,
( ~ p21(f5(f7(f10(c24,f12(c28,X39)),X38),X40),X41)
| p21(f5(X38,f14(f16(f18(f20(c29,X39),X40),X38),X41)),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_36) ).
fof(f35_nnf,plain,
! [X38,X39,X40,X41] :
( ~ p21(f5(f7(f10(c24,f12(c28,X39)),X38),X40),X41)
| p21(f5(X38,f14(f16(f18(f20(c29,X39),X40),X38),X41)),X41) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [X38,X39,X40,X41] :
( ~ p21(f5(f7(f10(c24,f12(c28,X39)),X38),X40),X41)
| p21(f5(X38,f14(f16(f18(f20(c29,X39),X40),X38),X41)),X41) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
( ~ p21(f5(f7(f10(c24,f12(c28,X1)),X0),X2),X3)
| p21(f5(X0,f14(f16(f18(f20(c29,X1),X2),X0),X3)),X3) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi34,negated_conjecture,
ifeq(p21(f5(f7(f10(c24,f12(c28,X0)),X1),X2),X3),true,p21(f5(X1,f14(f16(f18(f20(c29,X0),X2),X1),X3)),X3),true) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(f23,negated_conjecture,
p21(f5(f7(f10(c24,f12(c28,f12(c25,c26))),c22),c23),c27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_24) ).
fof(f23_nnf,plain,
p21(f5(f7(f10(c24,f12(c28,f12(c25,c26))),c22),c23),c27),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
p21(f5(f7(f10(c24,f12(c28,f12(c25,c26))),c22),c23),c27),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,negated_conjecture,
p21(f5(f7(f10(c24,f12(c28,f12(c25,c26))),c22),c23),c27) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h1,plain,
p21(f5(c22,f14(f16(f18(f20(c29,f12(c25,c26)),c23),c22),c27)),c27) = true,
inference(hyper_resolution,[status(thm)],[hi34,hi23]) ).
cnf(f37,negated_conjecture,
( ~ p21(f5(f7(f10(c24,f12(c28,X39)),X38),X40),X41)
| p21(f5(f7(f10(c24,X39),X38),X40),f14(f16(f18(f20(c29,X39),X40),X38),X41)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_38) ).
fof(f37_nnf,plain,
! [X39,X38,X40,X41] :
( ~ p21(f5(f7(f10(c24,f12(c28,X39)),X38),X40),X41)
| p21(f5(f7(f10(c24,X39),X38),X40),f14(f16(f18(f20(c29,X39),X40),X38),X41)) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [X39,X38,X40,X41] :
( ~ p21(f5(f7(f10(c24,f12(c28,X39)),X38),X40),X41)
| p21(f5(f7(f10(c24,X39),X38),X40),f14(f16(f18(f20(c29,X39),X40),X38),X41)) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
( ~ p21(f5(f7(f10(c24,f12(c28,X0)),X1),X2),X3)
| p21(f5(f7(f10(c24,X0),X1),X2),f14(f16(f18(f20(c29,X0),X2),X1),X3)) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi36,negated_conjecture,
ifeq(p21(f5(f7(f10(c24,f12(c28,X0)),X1),X2),X3),true,p21(f5(f7(f10(c24,X0),X1),X2),f14(f16(f18(f20(c29,X0),X2),X1),X3)),true) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(h3,plain,
p21(f5(f7(f10(c24,f12(c25,c26)),c22),c23),f14(f16(f18(f20(c29,f12(c25,c26)),c23),c22),c27)) = true,
inference(hyper_resolution,[status(thm)],[hi36,hi23]) ).
cnf(f32,negated_conjecture,
( ~ p21(f5(f7(f10(c24,f12(c25,c26)),X42),X43),X44)
| p3(X43,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_33) ).
fof(f32_nnf,plain,
! [X43,X44,X42] :
( ~ p21(f5(f7(f10(c24,f12(c25,c26)),X42),X43),X44)
| p3(X43,X44) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X43,X44,X42] :
( ~ p21(f5(f7(f10(c24,f12(c25,c26)),X42),X43),X44)
| p3(X43,X44) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
( ~ p21(f5(f7(f10(c24,f12(c25,c26)),X2),X0),X1)
| p3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(hi32,negated_conjecture,
ifeq(p21(f5(f7(f10(c24,f12(c25,c26)),X0),X1),X2),true,p3(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h7,plain,
p3(c23,f14(f16(f18(f20(c29,f12(c25,c26)),c23),c22),c27)) = true,
inference(hyper_resolution,[status(thm)],[hi32,h3]) ).
cnf(f16,negated_conjecture,
( ~ p3(X46,X48)
| ~ p3(X46,X47)
| p3(X47,X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_17) ).
fof(f16_nnf,plain,
! [X47,X48,X46] :
( ~ p3(X46,X48)
| ~ p3(X46,X47)
| p3(X47,X48) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X47,X48,X46] :
( ~ p3(X46,X48)
| ~ p3(X46,X47)
| p3(X47,X48) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ p3(X2,X1)
| ~ p3(X2,X0)
| p3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,negated_conjecture,
ifeq(p3(X0,X1),true,ifeq(p3(X0,X2),true,p3(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h12,plain,
p3(f14(f16(f18(f20(c29,f12(c25,c26)),c23),c22),c27),c23) = true,
inference(hyper_resolution,[status(thm)],[hi16,h7,hi5]) ).
cnf(f30,negated_conjecture,
( ~ p3(X57,X59)
| ~ p2(X56,X58)
| p4(f5(X56,X57),f5(X58,X59)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_31) ).
fof(f30_nnf,plain,
! [X56,X57,X58,X59] :
( ~ p3(X57,X59)
| ~ p2(X56,X58)
| p4(f5(X56,X57),f5(X58,X59)) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X56,X57,X58,X59] :
( ~ p3(X57,X59)
| ~ p2(X56,X58)
| p4(f5(X56,X57),f5(X58,X59)) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ p3(X1,X3)
| ~ p2(X0,X2)
| p4(f5(X0,X1),f5(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi30,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)],[c30]) ).
cnf(f6,negated_conjecture,
p2(X27,X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_7) ).
fof(f6_nnf,plain,
! [X27] : p2(X27,X27),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X27] : p2(X27,X27),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h14,plain,
p4(f5(V0,f14(f16(f18(f20(c29,f12(c25,c26)),c23),c22),c27)),f5(V0,c23)) = true,
inference(hyper_resolution,[status(thm)],[hi30,hi6,h12]) ).
cnf(f22,negated_conjecture,
( ~ p21(X36,X37)
| ~ p4(X36,X34)
| ~ p3(X37,X35)
| p21(X34,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_23) ).
fof(f22_nnf,plain,
! [X34,X35,X37,X36] :
( ~ p21(X36,X37)
| ~ p4(X36,X34)
| ~ p3(X37,X35)
| p21(X34,X35) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X34,X35,X37,X36] :
( ~ p21(X36,X37)
| ~ p4(X36,X34)
| ~ p3(X37,X35)
| p21(X34,X35) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( ~ p21(X3,X2)
| ~ p4(X3,X0)
| ~ p3(X2,X1)
| p21(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi22,negated_conjecture,
ifeq(p3(X0,X1),true,ifeq(p4(X2,X3),true,ifeq(p21(X2,X0),true,p21(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h21,plain,
p21(f5(c22,c23),c27) = true,
inference(hyper_resolution,[status(thm)],[hi22,hi5,h14,h1]) ).
cnf(f34,negated_conjecture,
( ~ p21(f5(f7(f10(c24,f12(c25,c26)),c22),X77),c27)
| ~ p21(f5(c22,c23),X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p21_35) ).
fof(f34_nnf,plain,
! [X77] :
( ~ p21(f5(f7(f10(c24,f12(c25,c26)),c22),X77),c27)
| ~ p21(f5(c22,c23),X77) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X77] :
( ~ p21(f5(f7(f10(c24,f12(c25,c26)),c22),X77),c27)
| ~ p21(f5(c22,c23),X77) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
( ~ p21(f5(f7(f10(c24,f12(c25,c26)),c22),X0),c27)
| ~ p21(f5(c22,c23),X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi37,negated_conjecture,
ifeq(p21(f5(c22,c23),X0),true,ifeq(p21(f5(f7(f10(c24,f12(c25,c26)),c22),X0),c27),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi37,h21,h0]) ).
cnf(t321,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t321]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN632-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.39 % Computer : n005.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Fri Sep 25 01:56:24 UTC 2026
% 0.15/5.40 % CPUTime :
% 0.15/5.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.89/6.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.89/6.44 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------