%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN558-1 : 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 03:35:11 PM UTC 2026
% Result : Unsatisfiable 6.47s 1.37s
% Output : Proof 6.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 41 unt; 0 def)
% Number of atoms : 101 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 90 ( 3 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,negated_conjecture,
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_11) ).
fof(f10_nnf,plain,
! [X11,X12,X13,X14] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X11,X12,X13,X14] :
( ~ p5(X11,X14,X13)
| ~ p5(X11,X12,X14)
| p5(X11,X12,X13) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ p5(X0,X3,X2)
| ~ p5(X0,X1,X3)
| p5(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(p5(X0,X1,X2),true,ifeq(p5(X0,X2,X3),true,p5(X0,X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f3,negated_conjecture,
p5(c7,c10,c9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_4) ).
fof(f3_nnf,plain,
p5(c7,c10,c9),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
p5(c7,c10,c9),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi3,negated_conjecture,
p5(c7,c10,c9) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f5,negated_conjecture,
p5(c7,X21,f3(X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_6) ).
fof(f5_nnf,plain,
! [X21] : p5(c7,X21,f3(X21)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X21] : p5(c7,X21,f3(X21)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
p5(c7,X0,f3(X0)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,negated_conjecture,
p5(c7,X0,f3(X0)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h2,plain,
p5(c7,c10,f3(c9)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi3,hi5]) ).
cnf(f4,negated_conjecture,
p5(c7,c10,c8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_5) ).
fof(f4_nnf,plain,
p5(c7,c10,c8),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p5(c7,c10,c8),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
p5(c7,c10,c8) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h1,plain,
p5(c7,c10,f3(c8)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi4,hi5]) ).
cnf(f12,negated_conjecture,
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_13) ).
fof(f12_nnf,plain,
! [X3,X4,X5] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X3,X4,X5] :
( ~ p5(c7,X5,X3)
| ~ p5(c7,X5,X4)
| ~ p6(c7,X3)
| ~ p6(c7,X4)
| p2(X3,X4) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( ~ p5(c7,X2,X0)
| ~ p5(c7,X2,X1)
| ~ p6(c7,X0)
| ~ p6(c7,X1)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi11,negated_conjecture,
ifeq(p6(c7,X0),true,ifeq(p6(c7,X1),true,ifeq(p5(c7,X2,X0),true,ifeq(p5(c7,X2,X1),true,p2(X1,X0),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f2,negated_conjecture,
p6(c7,f3(X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_3) ).
fof(f2_nnf,plain,
! [X21] : p6(c7,f3(X21)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X21] : p6(c7,f3(X21)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
p6(c7,f3(X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
p6(c7,f3(X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h6,plain,
p2(f3(c9),f3(c8)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,h1,h2]) ).
cnf(f13,negated_conjecture,
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_14) ).
fof(f13_nnf,plain,
! [X15,X16,X17,X18,X19,X20] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X15,X16,X17,X18,X19,X20] :
( ~ p5(X20,X18,X19)
| ~ p4(X20,X15)
| ~ p2(X19,X17)
| ~ p2(X18,X16)
| p5(X15,X16,X17) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ p5(X5,X3,X4)
| ~ p4(X5,X0)
| ~ p2(X4,X2)
| ~ p2(X3,X1)
| p5(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi12,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X2,X3),true,ifeq(p4(X4,X5),true,ifeq(p5(X4,X0,X2),true,p5(X5,X1,X3),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f0,negated_conjecture,
p2(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
fof(f0_nnf,plain,
! [X0] : p2(X0,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0] : p2(X0,X0),
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(f1,negated_conjecture,
p4(X8,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_2) ).
fof(f1_nnf,plain,
! [X8] : p4(X8,X8),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X8] : p4(X8,X8),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p4(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
p4(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h16,plain,
p5(c7,c9,f3(c8)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi0,h6,hi1,hi5]) ).
cnf(f7,negated_conjecture,
( ~ p5(c7,c9,X26)
| ~ p5(c7,c8,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p5_8) ).
fof(f7_nnf,plain,
! [X26] :
( ~ p5(c7,c9,X26)
| ~ p5(c7,c8,X26) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X26] :
( ~ p5(c7,c9,X26)
| ~ p5(c7,c8,X26) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ p5(c7,c9,X0)
| ~ p5(c7,c8,X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi13,negated_conjecture,
ifeq(p5(c7,c8,X0),true,ifeq(p5(c7,c9,X0),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi13,hi5,h16]) ).
cnf(t341,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t341]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN558-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 01:45:19 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.47/1.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.47/1.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------