%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG365-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 12:52:24 PM UTC 2026
% Result : Unsatisfiable 10.61s 2.13s
% Output : Proof 10.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 45 unt; 0 def)
% Number of atoms : 53 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 25 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-5 aty)
% Number of variables : 19 ( 5 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f386,negated_conjecture,
( ~ c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),V_x,tc_RealDef_Oreal)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f386_nnf,plain,
! [V_x] :
( ~ c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),V_x,tc_RealDef_Oreal)
| v_thesis____ ),
inference(nnf_transformation,[status(thm)],[f386]) ).
fof(f386_sk,plain,
! [V_x] :
( ~ c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),V_x,tc_RealDef_Oreal)
| v_thesis____ ),
inference(skolemisation,[status(esa)],[f386_nnf]) ).
cnf(c386,plain,
( ~ c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),X0,tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnf_transformation,[status(esa)],[f386_sk]) ).
cnf(hi383,negated_conjecture,
ifeq(c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),X0,tc_RealDef_Oreal),true,v_thesis____,true) = true,
inference(equality_encoding,[status(esa)],[c386]) ).
cnf(f384,axiom,
c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),v_sko__CHAINED__1(v_f____,v_ga____,v_s),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f384_nnf,plain,
c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),v_sko__CHAINED__1(v_f____,v_ga____,v_s),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f384]) ).
cnf(c384,plain,
c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),v_sko__CHAINED__1(v_f____,v_ga____,v_s),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f384_nnf]) ).
cnf(hi382,axiom,
c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),v_sko__CHAINED__1(v_f____,v_ga____,v_s),tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c384]) ).
cnf(t2,plain,
v_thesis____ = true,
inference(hyper_resolution,[status(thm)],[hi383,hi382]) ).
cnf(t824,plain,
true = v_thesis____,
inference(orient,[status(thm)],[t2]) ).
cnf(f369,axiom,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conv2_0) ).
fof(f369_nnf,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f369]) ).
cnf(c369,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f369_nnf]) ).
cnf(t82,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c369]) ).
cnf(t812,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t82]) ).
cnf(t1003,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = v_thesis____,
inference(step,[status(thm)],[t812,t824]) ).
cnf(t851,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = v_thesis____,
inference(orient,[status(thm)],[t1003]) ).
cnf(f343,axiom,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conv1_0) ).
fof(f343_nnf,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f343]) ).
cnf(c343,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f343_nnf]) ).
cnf(t41,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c343]) ).
cnf(t818,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t1005,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = v_thesis____,
inference(step,[status(thm)],[t818,t824]) ).
cnf(t853,plain,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = v_thesis____,
inference(orient,[status(thm)],[t1005]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t234,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(f55,axiom,
V_n != hAPP(c_Suc,V_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f55_nnf,plain,
! [V_n] : V_n != hAPP(c_Suc,V_n),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [V_n] : V_n != hAPP(c_Suc,V_n),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c55,plain,
X0 != hAPP(c_Suc,X0),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(f56,axiom,
hAPP(c_Suc,V_n) != V_n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f56_nnf,plain,
! [V_n] : hAPP(c_Suc,V_n) != V_n,
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [V_n] : hAPP(c_Suc,V_n) != V_n,
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
hAPP(c_Suc,X0) != X0,
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(f385,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f385_nnf,plain,
~ v_thesis____,
inference(nnf_transformation,[status(thm)],[f385]) ).
fof(f385_sk,plain,
~ v_thesis____,
inference(skolemisation,[status(esa)],[f385_nnf]) ).
cnf(c385,plain,
~ v_thesis____,
inference(cnf_transformation,[status(esa)],[f385_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c55,c56,c385]) ).
cnf(g0_0,plain,
true != ifeq(v_thesis____,true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(v_thesis____,true,false,c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
true != ifeq(v_thesis____,c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),false,c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)),
inference(rw,[status(thm)],[g0_1]) ).
cnf(g0_3,plain,
true != ifeq(true,c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),false,c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)),
inference(rw,[status(thm)],[g0_2,t824]) ).
cnf(g0_4,plain,
true != ifeq(true,c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),false,v_thesis____),
inference(rw,[status(thm)],[g0_3,t851]) ).
cnf(g0_5,plain,
true != ifeq(true,v_thesis____,false,v_thesis____),
inference(rw,[status(thm)],[g0_4,t853]) ).
cnf(g0_6,plain,
true != ifeq(v_thesis____,v_thesis____,false,v_thesis____),
inference(rw,[status(thm)],[g0_5,t824]) ).
cnf(g0_7,plain,
true != false,
inference(rw,[status(thm)],[g0_6,t234]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG365-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.39 % Computer : n026.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Fri Sep 25 05:31:55 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.61/2.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.61/2.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------