%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN556-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 222.77s 28.53s
% Output : Proof 222.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 42 unt; 0 def)
% Number of atoms : 94 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 95 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,negated_conjecture,
p2(c10,c13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_3) ).
fof(f2_nnf,plain,
p2(c10,c13),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
p2(c10,c13),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,negated_conjecture,
p2(c10,c13) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h2,plain,
p2(c10,c13) = true,
inference(hyper_resolution,[status(thm)],[hi2]) ).
cnf(f1,negated_conjecture,
p3(X15,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_2) ).
fof(f1_nnf,plain,
! [X15] : p3(X15,X15),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X15] : p3(X15,X15),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p3(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
p3(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h3,plain,
p3(c11,c11) = true,
inference(hyper_resolution,[status(thm)],[hi1]) ).
cnf(f10,negated_conjecture,
( ~ p3(X11,X13)
| ~ p2(X12,X14)
| p2(f8(X11,X12),f8(X13,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
fof(f10_nnf,plain,
! [X11,X12,X13,X14] :
( ~ p3(X11,X13)
| ~ p2(X12,X14)
| p2(f8(X11,X12),f8(X13,X14)) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X11,X12,X13,X14] :
( ~ p3(X11,X13)
| ~ p2(X12,X14)
| p2(f8(X11,X12),f8(X13,X14)) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ p3(X0,X2)
| ~ p2(X1,X3)
| p2(f8(X0,X1),f8(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p3(X2,X3),true,p2(f8(X2,X0),f8(X3,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h8,plain,
p2(f8(c11,c10),f8(c11,c13)) = true,
inference(hyper_resolution,[status(thm)],[hi9,h2,h3]) ).
cnf(f9,negated_conjecture,
( ~ p2(X4,X6)
| ~ p2(X3,X5)
| p2(f5(X3,X4),f5(X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_10) ).
fof(f9_nnf,plain,
! [X3,X4,X5,X6] :
( ~ p2(X4,X6)
| ~ p2(X3,X5)
| p2(f5(X3,X4),f5(X5,X6)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X3,X4,X5,X6] :
( ~ p2(X4,X6)
| ~ p2(X3,X5)
| p2(f5(X3,X4),f5(X5,X6)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ p2(X1,X3)
| ~ p2(X0,X2)
| p2(f5(X0,X1),f5(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X2,X3),true,p2(f5(X0,X2),f5(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
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(h9,plain,
p2(f5(f8(c11,c10),f6(f7(c12))),f5(f8(c11,c13),f6(f7(c12)))) = true,
inference(hyper_resolution,[status(thm)],[hi8,h8,hi0]) ).
cnf(f11,negated_conjecture,
( ~ p2(X18,X21)
| ~ p3(X20,X23)
| ~ p2(X19,X22)
| p3(f4(X18,X19,X20),f4(X21,X22,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_12) ).
fof(f11_nnf,plain,
! [X18,X19,X20,X21,X22,X23] :
( ~ p2(X18,X21)
| ~ p3(X20,X23)
| ~ p2(X19,X22)
| p3(f4(X18,X19,X20),f4(X21,X22,X23)) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X18,X19,X20,X21,X22,X23] :
( ~ p2(X18,X21)
| ~ p3(X20,X23)
| ~ p2(X19,X22)
| p3(f4(X18,X19,X20),f4(X21,X22,X23)) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ p2(X0,X3)
| ~ p3(X2,X5)
| ~ p2(X1,X4)
| p3(f4(X0,X1,X2),f4(X3,X4,X5)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p3(X2,X3),true,ifeq(p2(X4,X5),true,p3(f4(X4,X0,X2),f4(X5,X1,X3)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h10,plain,
p3(f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11),f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11)) = true,
inference(hyper_resolution,[status(thm)],[hi10,h9,h3,h2]) ).
cnf(f6,negated_conjecture,
( ~ p3(X15,X17)
| ~ p3(X15,X16)
| p3(X16,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_7) ).
fof(f6_nnf,plain,
! [X16,X17,X15] :
( ~ p3(X15,X17)
| ~ p3(X15,X16)
| p3(X16,X17) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X16,X17,X15] :
( ~ p3(X15,X17)
| ~ p3(X15,X16)
| p3(X16,X17) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ p3(X2,X1)
| ~ p3(X2,X0)
| p3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(p3(X0,X1),true,ifeq(p3(X0,X2),true,p3(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h11,plain,
p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h10,hi1]) ).
cnf(h0,plain,
p3(c9,c9) = true,
inference(hyper_resolution,[status(thm)],[hi1]) ).
cnf(f7,negated_conjecture,
p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_8) ).
fof(f7_nnf,plain,
p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11)),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11)),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,negated_conjecture,
p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h4,plain,
p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi7,h0]) ).
cnf(h5,plain,
p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi1,h4]) ).
cnf(h6,plain,
p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi1,h5]) ).
cnf(h7,plain,
p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi1,h6]) ).
cnf(t6,plain,
p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h7,h11]) ).
cnf(t48,plain,
p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f8,negated_conjecture,
~ p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p3_9) ).
fof(f8_nnf,plain,
~ p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t48]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN556-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 01:43:42 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 222.77/28.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 222.77/28.53 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------