%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN572-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 03:35:13 PM UTC 2026
% Result : Unsatisfiable 35.26s 5.16s
% Output : Proof 35.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 61 unt; 0 def)
% Number of atoms : 133 ( 28 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 : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 172 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,negated_conjecture,
( ~ p4(X22,X24)
| ~ p4(X22,X23)
| p4(X23,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_14) ).
fof(f13_nnf,plain,
! [X23,X24,X22] :
( ~ p4(X22,X24)
| ~ p4(X22,X23)
| p4(X23,X24) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X23,X24,X22] :
( ~ p4(X22,X24)
| ~ p4(X22,X23)
| p4(X23,X24) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ p4(X2,X1)
| ~ p4(X2,X0)
| p4(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X0,X2),true,p4(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f3,negated_conjecture,
p4(f10(f9(X27)),f10(X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_4) ).
fof(f3_nnf,plain,
! [X27] : p4(f10(f9(X27)),f10(X27)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X27] : p4(f10(f9(X27)),f10(X27)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p4(f10(f9(X0)),f10(X0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
p4(f10(f9(X0)),f10(X0)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f2,negated_conjecture,
p4(X22,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_3) ).
fof(f2_nnf,plain,
! [X22] : p4(X22,X22),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X22] : p4(X22,X22),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
p4(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
p4(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h3,plain,
p4(f10(V0),f10(f9(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi3,hi2]) ).
cnf(h10,plain,
p4(f10(V0),f10(f9(f9(V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi3,h3]) ).
cnf(f18,negated_conjecture,
( ~ p4(X29,X31)
| ~ p4(X28,X30)
| p4(f11(X28,X29),f11(X30,X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_19) ).
fof(f18_nnf,plain,
! [X28,X29,X30,X31] :
( ~ p4(X29,X31)
| ~ p4(X28,X30)
| p4(f11(X28,X29),f11(X30,X31)) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X28,X29,X30,X31] :
( ~ p4(X29,X31)
| ~ p4(X28,X30)
| p4(f11(X28,X29),f11(X30,X31)) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ p4(X1,X3)
| ~ p4(X0,X2)
| p4(f11(X0,X1),f11(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi17,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X2,X3),true,p4(f11(X0,X2),f11(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h13,plain,
p4(f11(V0,f10(V1)),f11(V0,f10(f9(f9(V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi2,h10]) ).
cnf(f17,negated_conjecture,
( ~ p12(X2,X3)
| ~ p4(X3,X1)
| ~ p4(X2,X0)
| p12(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_18) ).
fof(f17_nnf,plain,
! [X0,X1,X2,X3] :
( ~ p12(X2,X3)
| ~ p4(X3,X1)
| ~ p4(X2,X0)
| p12(X0,X1) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X0,X1,X2,X3] :
( ~ p12(X2,X3)
| ~ p4(X3,X1)
| ~ p4(X2,X0)
| p12(X0,X1) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( ~ p12(X2,X3)
| ~ p4(X3,X1)
| ~ p4(X2,X0)
| p12(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi16,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X2,X3),true,ifeq(p12(X0,X2),true,p12(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(f14,negated_conjecture,
p12(f10(f3(X4,X5)),f11(f10(X4),f10(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_15) ).
fof(f14_nnf,plain,
! [X4,X5] : p12(f10(f3(X4,X5)),f11(f10(X4),f10(X5))),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X4,X5] : p12(f10(f3(X4,X5)),f11(f10(X4),f10(X5))),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
p12(f10(f3(X0,X1)),f11(f10(X0),f10(X1))),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,negated_conjecture,
p12(f10(f3(X0,X1)),f11(f10(X0),f10(X1))) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h166,plain,
p12(f10(f3(V0,V1)),f11(f10(V0),f10(f9(f9(V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi16,hi2,h13,hi14]) ).
cnf(h16,plain,
p4(f10(f9(f9(f9(V0)))),f10(V0)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h10,hi3]) ).
cnf(h41,plain,
p4(f11(V0,f10(f9(f9(f9(V1))))),f11(V0,f10(V1))) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi2,h16]) ).
cnf(f11,negated_conjecture,
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
fof(f11_nnf,plain,
! [X7,X8,X6] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X7,X8,X6] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X0,X2),true,p2(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f10,negated_conjecture,
p2(f3(X14,f9(X14)),f5(f7(f8(c13)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
fof(f10_nnf,plain,
! [X14] : p2(f3(X14,f9(X14)),f5(f7(f8(c13)))),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X14] : p2(f3(X14,f9(X14)),f5(f7(f8(c13)))),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
p2(f3(X0,f9(X0)),f5(f7(f8(c13)))),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,negated_conjecture,
p2(f3(X0,f9(X0)),f5(f7(f8(c13)))) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f0,negated_conjecture,
p2(X6,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
fof(f0_nnf,plain,
! [X6] : p2(X6,X6),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X6] : p2(X6,X6),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h58,plain,
p2(f5(f7(f8(c13))),f3(V0,f9(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi10,hi0]) ).
cnf(f19,negated_conjecture,
( ~ p2(X10,X12)
| ~ p2(X9,X11)
| p2(f3(X9,X10),f3(X11,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_20) ).
fof(f19_nnf,plain,
! [X9,X10,X11,X12] :
( ~ p2(X10,X12)
| ~ p2(X9,X11)
| p2(f3(X9,X10),f3(X11,X12)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X9,X10,X11,X12] :
( ~ p2(X10,X12)
| ~ p2(X9,X11)
| p2(f3(X9,X10),f3(X11,X12)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ p2(X1,X3)
| ~ p2(X0,X2)
| p2(f3(X0,X1),f3(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi18,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X2,X3),true,p2(f3(X0,X2),f3(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h79,plain,
p2(f3(V0,f5(f7(f8(c13)))),f3(V0,f3(V1,f9(V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi0,h58]) ).
cnf(f4,negated_conjecture,
p2(f3(X13,f5(f7(f8(c13)))),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_5) ).
fof(f4_nnf,plain,
! [X13] : p2(f3(X13,f5(f7(f8(c13)))),X13),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X13] : p2(f3(X13,f5(f7(f8(c13)))),X13),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
p2(f3(X0,f5(f7(f8(c13)))),X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
p2(f3(X0,f5(f7(f8(c13)))),X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h2310,plain,
p2(f3(V0,f3(V1,f9(V1))),V0) = true,
inference(hyper_resolution,[status(thm)],[hi11,h79,hi4]) ).
cnf(f16,negated_conjecture,
p2(f3(X15,f3(X16,X17)),f3(f3(X15,X16),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_17) ).
fof(f16_nnf,plain,
! [X15,X16,X17] : p2(f3(X15,f3(X16,X17)),f3(f3(X15,X16),X17)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X15,X16,X17] : p2(f3(X15,f3(X16,X17)),f3(f3(X15,X16),X17)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
p2(f3(X0,f3(X1,X2)),f3(f3(X0,X1),X2)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi15,negated_conjecture,
p2(f3(X0,f3(X1,X2)),f3(f3(X0,X1),X2)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h2322,plain,
p2(f3(f3(V0,V1),f9(V1)),V0) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi15,h2310]) ).
cnf(f8,negated_conjecture,
( ~ p2(X25,X26)
| p4(f10(X25),f10(X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_9) ).
fof(f8_nnf,plain,
! [X25,X26] :
( ~ p2(X25,X26)
| p4(f10(X25),f10(X26)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X25,X26] :
( ~ p2(X25,X26)
| p4(f10(X25),f10(X26)) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ p2(X0,X1)
| p4(f10(X0),f10(X1)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p2(X0,X1),true,p4(f10(X0),f10(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h2345,plain,
p4(f10(f3(f3(V0,V1),f9(V1))),f10(V0)) = true,
inference(hyper_resolution,[status(thm)],[hi8,h2322]) ).
cnf(t7,plain,
p12(f10(X1),f11(f10(f3(X1,X2)),f10(X2))) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2345,h41,h166]) ).
cnf(t257,plain,
p12(f10(X1),f11(f10(f3(X1,X2)),f10(X2))) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f15,negated_conjecture,
~ p12(f10(c14),f11(f10(f3(c14,c15)),f10(c15))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p12_16) ).
fof(f15_nnf,plain,
~ p12(f10(c14),f11(f10(f3(c14,c15)),f10(c15))),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ p12(f10(c14),f11(f10(f3(c14,c15)),f10(c15))),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ p12(f10(c14),f11(f10(f3(c14,c15)),f10(c15))),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(goal_0,negated_conjecture,
p12(f10(c14),f11(f10(f3(c14,c15)),f10(c15))) != true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t257]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN572-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 01:47:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 35.26/5.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.26/5.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------