%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN563-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 03:35:12 PM UTC 2026
% Result : Unsatisfiable 4.73s 1.51s
% Output : Proof 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 48 unt; 0 def)
% Number of atoms : 100 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 42 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 81 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,negated_conjecture,
~ p6(f4(c7),f3(f4(c8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p6_5) ).
fof(f4_nnf,plain,
~ p6(f4(c7),f3(f4(c8))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ p6(f4(c7),f3(f4(c8))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ p6(f4(c7),f3(f4(c8))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t212,plain,
ifeq(p6(f4(c7),f3(f4(c8))),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f8,negated_conjecture,
( ~ p6(c7,X27)
| p6(c7,f3(X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_9) ).
fof(f8_nnf,plain,
! [X27] :
( ~ p6(c7,X27)
| p6(c7,f3(X27)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X27] :
( ~ p6(c7,X27)
| p6(c7,f3(X27)) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ p6(c7,X0)
| p6(c7,f3(X0)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(p6(c7,X0),true,p6(c7,f3(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f1,negated_conjecture,
p6(X22,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_2) ).
fof(f1_nnf,plain,
! [X22] : p6(X22,X22),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X22] : p6(X22,X22),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p6(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
p6(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h2,plain,
p6(c7,f3(c7)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi1]) ).
cnf(h13,plain,
p6(c7,f3(f3(c7))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h2]) ).
cnf(f14,negated_conjecture,
( ~ p6(X7,X9)
| ~ p5(X9,X8)
| p5(X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_15) ).
fof(f14_nnf,plain,
! [X7,X8,X9] :
( ~ p6(X7,X9)
| ~ p5(X9,X8)
| p5(X7,X8) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X7,X8,X9] :
( ~ p6(X7,X9)
| ~ p5(X9,X8)
| p5(X7,X8) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ p6(X0,X2)
| ~ p5(X2,X1)
| p5(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi12,negated_conjecture,
ifeq(p5(X0,X1),true,ifeq(p6(X2,X0),true,p5(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f6,negated_conjecture,
p5(f3(f3(X16)),f3(f4(X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_7) ).
fof(f6_nnf,plain,
! [X16] : p5(f3(f3(X16)),f3(f4(X16))),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X16] : p5(f3(f3(X16)),f3(f4(X16))),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
p5(f3(f3(X0)),f3(f4(X0))),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,negated_conjecture,
p5(f3(f3(X0)),f3(f4(X0))) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h75,plain,
p5(c7,f3(f4(c7))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi4,h13]) ).
cnf(f10,negated_conjecture,
( ~ p2(X3,X4)
| p2(f3(X3),f3(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_11) ).
fof(f10_nnf,plain,
! [X3,X4] :
( ~ p2(X3,X4)
| p2(f3(X3),f3(X4)) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X3,X4] :
( ~ p2(X3,X4)
| p2(f3(X3),f3(X4)) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ p2(X0,X1)
| p2(f3(X0),f3(X1)) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p2(X0,X1),true,p2(f3(X0),f3(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f3,negated_conjecture,
p2(f4(c7),f4(c8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
fof(f3_nnf,plain,
p2(f4(c7),f4(c8)),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
p2(f4(c7),f4(c8)),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi2,negated_conjecture,
p2(f4(c7),f4(c8)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h10,plain,
p2(f3(f4(c7)),f3(f4(c8))) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi2]) ).
cnf(f16,negated_conjecture,
( ~ p2(X14,X12)
| ~ p5(X14,X15)
| ~ p2(X15,X13)
| p5(X12,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_17) ).
fof(f16_nnf,plain,
! [X12,X13,X15,X14] :
( ~ p2(X14,X12)
| ~ p5(X14,X15)
| ~ p2(X15,X13)
| p5(X12,X13) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X12,X13,X15,X14] :
( ~ p2(X14,X12)
| ~ p5(X14,X15)
| ~ p2(X15,X13)
| p5(X12,X13) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ p2(X3,X0)
| ~ p5(X3,X2)
| ~ p2(X2,X1)
| p5(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi14,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p5(X2,X0),true,ifeq(p2(X2,X3),true,p5(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f0,negated_conjecture,
p2(X0,X0),
file('/export/starexec/sandbox/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(h237,plain,
p5(c7,f3(f4(c8))) = true,
inference(hyper_resolution,[status(thm)],[hi14,h10,h75,hi0]) ).
cnf(f9,negated_conjecture,
( ~ p5(X10,X11)
| p6(f4(X10),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_10) ).
fof(f9_nnf,plain,
! [X10,X11] :
( ~ p5(X10,X11)
| p6(f4(X10),X11) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X10,X11] :
( ~ p5(X10,X11)
| p6(f4(X10),X11) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ p5(X0,X1)
| p6(f4(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(p5(X0,X1),true,p6(f4(X0),X1),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t89,plain,
p6(f4(c7),f3(f4(c8))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h237]) ).
cnf(t269,plain,
p6(f4(c7),f3(f4(c8))) = true,
inference(orient,[status(thm)],[t89]) ).
cnf(t600,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t212,t269]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t601,plain,
false = true,
inference(step,[status(thm)],[t600,t256]) ).
cnf(t599,plain,
false = true,
inference(orient,[status(thm)],[t601]) ).
cnf(f2,negated_conjecture,
~ p6(f4(c7),c8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p6_3) ).
fof(f2_nnf,plain,
~ p6(f4(c7),c8),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ p6(f4(c7),c8),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ p6(f4(c7),c8),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t599]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN563-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 01:45:04 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.73/1.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.73/1.51 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------