%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN559-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 10.49s 1.94s
% Output : Proof 10.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 35 unt; 0 def)
% Number of atoms : 63 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,negated_conjecture,
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_8) ).
fof(f7_nnf,plain,
! [X1,X2,X0] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X1,X2,X0] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X0,X2),true,p2(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f5,negated_conjecture,
p2(f3(f4(c11),c12),c15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
fof(f5_nnf,plain,
p2(f3(f4(c11),c12),c15),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
p2(f3(f4(c11),c12),c15),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
p2(f3(f4(c11),c12),c15) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
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(h6,plain,
p2(c15,f3(f4(c11),c12)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi5,hi0]) ).
cnf(f4,negated_conjecture,
p2(f5(c14,c10),c15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_5) ).
fof(f4_nnf,plain,
p2(f5(c14,c10),c15),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p2(f5(c14,c10),c15),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
p2(f5(c14,c10),c15) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h2,plain,
p2(c15,f5(c14,c10)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi4,hi0]) ).
cnf(h8,plain,
p2(f5(c14,c10),f3(f4(c11),c12)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h2,h6]) ).
cnf(f13,negated_conjecture,
( ~ p2(f5(X25,c10),f3(f4(c11),c12))
| ~ p2(f6(c9,X26),X25)
| ~ p7(c10,X26)
| ~ p8(X26,c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p8_14) ).
fof(f13_nnf,plain,
! [X26,X25] :
( ~ p2(f5(X25,c10),f3(f4(c11),c12))
| ~ p2(f6(c9,X26),X25)
| ~ p7(c10,X26)
| ~ p8(X26,c9) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X26,X25] :
( ~ p2(f5(X25,c10),f3(f4(c11),c12))
| ~ p2(f6(c9,X26),X25)
| ~ p7(c10,X26)
| ~ p8(X26,c9) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ p2(f5(X1,c10),f3(f4(c11),c12))
| ~ p2(f6(c9,X0),X1)
| ~ p7(c10,X0)
| ~ p8(X0,c9) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,negated_conjecture,
ifeq(p8(X0,c9),true,ifeq(p7(c10,X0),true,ifeq(p2(f6(c9,X0),X1),true,ifeq(p2(f5(X1,c10),f3(f4(c11),c12)),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f1,negated_conjecture,
p8(c13,c9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_2) ).
fof(f1_nnf,plain,
p8(c13,c9),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
p8(c13,c9),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,negated_conjecture,
p8(c13,c9) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f2,negated_conjecture,
p7(c10,c13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_3) ).
fof(f2_nnf,plain,
p7(c10,c13),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
p7(c10,c13),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,negated_conjecture,
p7(c10,c13) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f3,negated_conjecture,
p2(f6(c9,c13),c14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
fof(f3_nnf,plain,
p2(f6(c9,c13),c14),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
p2(f6(c9,c13),c14),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi3,negated_conjecture,
p2(f6(c9,c13),c14) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi13,hi1,hi2,hi3,h8]) ).
cnf(t265,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t265]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN559-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 01:44:07 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.49/1.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.49/1.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------