%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN577-1 : 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 03:35:14 PM UTC 2026
% Result : Unsatisfiable 10.71s 6.96s
% Output : Proof 10.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 38 unt; 0 def)
% Number of atoms : 70 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,negated_conjecture,
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_14) ).
fof(f13_nnf,plain,
! [X1,X2,X0] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X1,X2,X0] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X0,X2),true,p2(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f11,negated_conjecture,
p2(f5(f6(c9),c20),c18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_12) ).
fof(f11_nnf,plain,
p2(f5(f6(c9),c20),c18),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
p2(f5(f6(c9),c20),c18),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,negated_conjecture,
p2(f5(f6(c9),c20),c18) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
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(h374,plain,
p2(c18,f5(f6(c9),c20)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi11,hi0]) ).
cnf(f7,negated_conjecture,
p2(f4(c16,c14),c18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_8) ).
fof(f7_nnf,plain,
p2(f4(c16,c14),c18),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
p2(f4(c16,c14),c18),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,negated_conjecture,
p2(f4(c16,c14),c18) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h26,plain,
p2(c18,f4(c16,c14)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi7,hi0]) ).
cnf(h523,plain,
p2(f4(c16,c14),f5(f6(c9),c20)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h26,h374]) ).
cnf(f10,negated_conjecture,
p2(f5(f6(c9),c19),c17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_11) ).
fof(f10_nnf,plain,
p2(f5(f6(c9),c19),c17),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
p2(f5(f6(c9),c19),c17),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,negated_conjecture,
p2(f5(f6(c9),c19),c17) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h309,plain,
p2(c17,f5(f6(c9),c19)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi10,hi0]) ).
cnf(f8,negated_conjecture,
p2(f4(c15,c14),c17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_9) ).
fof(f8_nnf,plain,
p2(f4(c15,c14),c17),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
p2(f4(c15,c14),c17),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi8,negated_conjecture,
p2(f4(c15,c14),c17) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h49,plain,
p2(c17,f4(c15,c14)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi8,hi0]) ).
cnf(h445,plain,
p2(f4(c15,c14),f5(f6(c9),c19)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h49,h309]) ).
cnf(f19,negated_conjecture,
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p7_20) ).
fof(f19_nnf,plain,
! [X34,X32,X33] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X34,X32,X33] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ p2(f4(X2,c14),f5(f6(X0),c20))
| ~ p2(f4(X1,c14),f5(f6(X0),c19))
| ~ p2(c16,X2)
| ~ p2(c15,X1)
| ~ p7(X0,c10) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi21,negated_conjecture,
ifeq(p7(X0,c10),true,ifeq(p2(c15,X1),true,ifeq(p2(c16,X2),true,ifeq(p2(f4(X1,c14),f5(f6(X0),c19)),true,ifeq(p2(f4(X2,c14),f5(f6(X0),c20)),true,false,true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f4,negated_conjecture,
p7(c9,c10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_5) ).
fof(f4_nnf,plain,
p7(c9,c10),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p7(c9,c10),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
p7(c9,c10) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi21,hi4,hi0,hi0,h445,h523]) ).
cnf(t4449,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4449]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN577-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n005.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 01:46:52 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.71/6.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.71/6.96 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------