%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HWV005-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 01:37:37 PM UTC 2026
% Result : Unsatisfiable 6.28s 1.75s
% Output : Proof 6.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 33
% Syntax : Number of formulae : 238 ( 154 unt; 0 def)
% Number of atoms : 358 ( 129 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 254 ( 134 ~; 120 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-4 aty)
% Number of variables : 141 ( 2 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( one(P2)
| ~ one(P1)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',value_propagation_one1) ).
fof(f1_nnf,plain,
! [P1,P2] :
( one(P2)
| ~ one(P1)
| ~ connection(P1,P2) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [P1,P2] :
( one(P2)
| ~ one(P1)
| ~ connection(P1,P2) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( one(X1)
| ~ one(X0)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t67,plain,
ifeq(connection(X1,X2),true,ifeq(one(X1),true,one(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t94,plain,
ifeq(connection(X1,X2),true,ifeq(one(X1),true,one(X2),true),true) = true,
inference(orient,[status(thm)],[t67]) ).
cnf(f21,axiom,
( one(out1(K))
| ~ zero(in1(K))
| ~ not_ok(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_0_1_fw) ).
fof(f21_nnf,plain,
! [K] :
( one(out1(K))
| ~ zero(in1(K))
| ~ not_ok(K) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [K] :
( one(out1(K))
| ~ zero(in1(K))
| ~ not_ok(K) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( one(out1(X0))
| ~ zero(in1(X0))
| ~ not_ok(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t77,plain,
ifeq(not_ok(X1),true,ifeq(zero(in1(X1)),true,one(out1(X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t131,plain,
ifeq(not_ok(X1),true,ifeq(zero(in1(X1)),true,one(out1(X1)),true),true) = true,
inference(orient,[status(thm)],[t77]) ).
cnf(f26,axiom,
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_ok_or_abnormal) ).
fof(f26_nnf,plain,
! [K] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [K] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( abnormal(X0)
| not_ok(X0)
| ~ logic_not(X0) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t52,plain,
ifeq(logic_not(X1),true,or(not_ok(X1),abnormal(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t140,plain,
ifeq(logic_not(X1),true,or(not_ok(X1),abnormal(X1)),true) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(f46,negated_conjecture,
~ abnormal(not1(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_not1) ).
fof(f46_nnf,plain,
~ abnormal(not1(h)),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
~ abnormal(not1(h)),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
~ abnormal(not1(h)),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(t4,plain,
abnormal(not1(h)) = false,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t354,plain,
abnormal(not1(h)) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t356,plain,
true = ifeq(logic_not(not1(h)),true,or(not_ok(not1(h)),false),true),
inference(cp,[status(thm)],[t140,t354]) ).
cnf(f29,axiom,
( logic_not(not1(X))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_not1) ).
fof(f29_nnf,plain,
! [X] :
( logic_not(not1(X))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X] :
( logic_not(not1(X))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( logic_not(not1(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(hi25,axiom,
ifeq(halfadder(X0),true,logic_not(not1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(f40,hypothesis,
halfadder(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_isa_halfadder) ).
fof(f40_nnf,plain,
halfadder(h),
inference(nnf_transformation,[status(thm)],[f40]) ).
cnf(c40,plain,
halfadder(h),
inference(cnf_transformation,[status(esa)],[f40_nnf]) ).
cnf(hi36,axiom,
halfadder(h) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t8,plain,
logic_not(not1(h)) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi36]) ).
cnf(t333,plain,
logic_not(not1(h)) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t1123,plain,
true = ifeq(true,true,or(not_ok(not1(h)),false),true),
inference(step,[status(thm)],[t356,t333]) ).
cnf(t25,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t87,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t25]) ).
cnf(t1124,plain,
true = or(not_ok(not1(h)),false),
inference(step,[status(thm)],[t1123,t87]) ).
cnf(t11,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t88,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t1125,plain,
true = not_ok(not1(h)),
inference(step,[status(thm)],[t1124,t88]) ).
cnf(t381,plain,
not_ok(not1(h)) = true,
inference(orient,[status(thm)],[t1125]) ).
cnf(t386,plain,
true = ifeq(true,true,ifeq(zero(in1(not1(h))),true,one(out1(not1(h))),true),true),
inference(cp,[status(thm)],[t131,t381]) ).
cnf(t1129,plain,
true = ifeq(zero(in1(not1(h))),true,one(out1(not1(h))),true),
inference(step,[status(thm)],[t386,t87]) ).
cnf(f36,axiom,
( connection(outc(X),out1(and2(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_connection_outc_out1and2) ).
fof(f36_nnf,plain,
! [X] :
( connection(outc(X),out1(and2(X)))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [X] :
( connection(outc(X),out1(and2(X)))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
( connection(outc(X0),out1(and2(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi32,axiom,
ifeq(halfadder(X0),true,connection(outc(X0),out1(and2(X0))),true) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(h3,plain,
connection(outc(h),out1(and2(h))) = true,
inference(hyper_resolution,[status(thm)],[hi32,hi36]) ).
cnf(f0,axiom,
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',value_propagation_zero1) ).
fof(f0_nnf,plain,
! [P1,P2] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [P1,P2] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( zero(X1)
| ~ zero(X0)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(connection(X0,X1),true,ifeq(zero(X0),true,zero(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f44,hypothesis,
zero(outc(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outc_0) ).
fof(f44_nnf,plain,
zero(outc(h)),
inference(nnf_transformation,[status(thm)],[f44]) ).
cnf(c44,plain,
zero(outc(h)),
inference(cnf_transformation,[status(esa)],[f44_nnf]) ).
cnf(hi40,axiom,
zero(outc(h)) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h17,plain,
zero(out1(and2(h))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,hi40]) ).
cnf(f38,axiom,
( connection(out1(and2(X)),in1(not1(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_connection_out1and2_in1not1) ).
fof(f38_nnf,plain,
! [X] :
( connection(out1(and2(X)),in1(not1(X)))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [X] :
( connection(out1(and2(X)),in1(not1(X)))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( connection(out1(and2(X0)),in1(not1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi34,axiom,
ifeq(halfadder(X0),true,connection(out1(and2(X0)),in1(not1(X0))),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h1,plain,
connection(out1(and2(h)),in1(not1(h))) = true,
inference(hyper_resolution,[status(thm)],[hi34,hi36]) ).
cnf(t20,plain,
zero(in1(not1(h))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,h17]) ).
cnf(t142,plain,
zero(in1(not1(h))) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t1130,plain,
true = ifeq(true,true,one(out1(not1(h))),true),
inference(step,[status(thm)],[t1129,t142]) ).
cnf(t1131,plain,
true = one(out1(not1(h))),
inference(step,[status(thm)],[t1130,t87]) ).
cnf(t400,plain,
one(out1(not1(h))) = true,
inference(orient,[status(thm)],[t1131]) ).
cnf(t403,plain,
true = ifeq(connection(out1(not1(h)),X1),true,ifeq(true,true,one(X1),true),true),
inference(cp,[status(thm)],[t94,t400]) ).
cnf(t1276,plain,
true = ifeq(connection(out1(not1(h)),X1),true,one(X1),true),
inference(step,[status(thm)],[t403,t87]) ).
cnf(t1038,plain,
ifeq(connection(out1(not1(h)),X1),true,one(X1),true) = true,
inference(orient,[status(thm)],[t1276]) ).
cnf(f39,axiom,
( connection(out1(not1(X)),in2(and1(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_connection_out1not1_in2and1) ).
fof(f39_nnf,plain,
! [X] :
( connection(out1(not1(X)),in2(and1(X)))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [X] :
( connection(out1(not1(X)),in2(and1(X)))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( connection(out1(not1(X0)),in2(and1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi35,axiom,
ifeq(halfadder(X0),true,connection(out1(not1(X0)),in2(and1(X0))),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t34,plain,
connection(out1(not1(h)),in2(and1(h))) = true,
inference(hyper_resolution,[status(thm)],[hi35,hi36]) ).
cnf(t278,plain,
connection(out1(not1(h)),in2(and1(h))) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t1039,plain,
true = ifeq(true,true,one(in2(and1(h))),true),
inference(cp,[status(thm)],[t1038,t278]) ).
cnf(t1277,plain,
true = one(in2(and1(h))),
inference(step,[status(thm)],[t1039,t87]) ).
cnf(t32,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t335,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t32]) ).
cnf(f4,axiom,
( ~ one(P)
| ~ zero(P) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_value) ).
fof(f4_nnf,plain,
! [P] :
( ~ one(P)
| ~ zero(P) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [P] :
( ~ one(P)
| ~ zero(P) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ one(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t44,plain,
or(not(zero(X1)),not(one(X1))) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t302,plain,
or(not(zero(X1)),not(one(X1))) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(f8,axiom,
( zero(in2(K))
| zero(in1(K))
| ~ zero(out1(K))
| ~ and_ok(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_0_00) ).
fof(f8_nnf,plain,
! [K] :
( zero(in2(K))
| zero(in1(K))
| ~ zero(out1(K))
| ~ and_ok(K) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [K] :
( zero(in2(K))
| zero(in1(K))
| ~ zero(out1(K))
| ~ and_ok(K) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( zero(in2(X0))
| zero(in1(X0))
| ~ zero(out1(X0))
| ~ and_ok(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t83,plain,
ifeq(and_ok(X1),true,ifeq(zero(out1(X1)),true,or(zero(in1(X1)),zero(in2(X1))),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t112,plain,
ifeq(and_ok(X1),true,ifeq(zero(out1(X1)),true,or(zero(in1(X1)),zero(in2(X1))),true),true) = true,
inference(orient,[status(thm)],[t83]) ).
cnf(f13,axiom,
( one(out1(K))
| ~ one(in1(K))
| ~ or_ok(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1x_1) ).
fof(f13_nnf,plain,
! [K] :
( one(out1(K))
| ~ one(in1(K))
| ~ or_ok(K) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [K] :
( one(out1(K))
| ~ one(in1(K))
| ~ or_ok(K) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( one(out1(X0))
| ~ one(in1(X0))
| ~ or_ok(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t79,plain,
ifeq(or_ok(X1),true,ifeq(one(in1(X1)),true,one(out1(X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t124,plain,
ifeq(or_ok(X1),true,ifeq(one(in1(X1)),true,one(out1(X1)),true),true) = true,
inference(orient,[status(thm)],[t79]) ).
cnf(f20,axiom,
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_ok_or_abnormal) ).
fof(f20_nnf,plain,
! [K] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [K] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( abnormal(X0)
| or_ok(X0)
| ~ logic_or(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t53,plain,
ifeq(logic_or(X1),true,or(or_ok(X1),abnormal(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t141,plain,
ifeq(logic_or(X1),true,or(or_ok(X1),abnormal(X1)),true) = true,
inference(orient,[status(thm)],[t53]) ).
cnf(f47,negated_conjecture,
~ abnormal(or1(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_or1) ).
fof(f47_nnf,plain,
~ abnormal(or1(h)),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
~ abnormal(or1(h)),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c47,plain,
~ abnormal(or1(h)),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(t5,plain,
abnormal(or1(h)) = false,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t336,plain,
abnormal(or1(h)) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t337,plain,
true = ifeq(logic_or(or1(h)),true,or(or_ok(or1(h)),false),true),
inference(cp,[status(thm)],[t141,t336]) ).
cnf(f30,axiom,
( logic_or(or1(X))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_or1) ).
fof(f30_nnf,plain,
! [X] :
( logic_or(or1(X))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X] :
( logic_or(or1(X))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( logic_or(or1(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi26,axiom,
ifeq(halfadder(X0),true,logic_or(or1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t9,plain,
logic_or(or1(h)) = true,
inference(hyper_resolution,[status(thm)],[hi26,hi36]) ).
cnf(t334,plain,
logic_or(or1(h)) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t1117,plain,
true = ifeq(true,true,or(or_ok(or1(h)),false),true),
inference(step,[status(thm)],[t337,t334]) ).
cnf(t1118,plain,
true = or(or_ok(or1(h)),false),
inference(step,[status(thm)],[t1117,t87]) ).
cnf(t1119,plain,
true = or_ok(or1(h)),
inference(step,[status(thm)],[t1118,t88]) ).
cnf(t365,plain,
or_ok(or1(h)) = true,
inference(orient,[status(thm)],[t1119]) ).
cnf(t368,plain,
true = ifeq(true,true,ifeq(one(in1(or1(h))),true,one(out1(or1(h))),true),true),
inference(cp,[status(thm)],[t124,t365]) ).
cnf(t1126,plain,
true = ifeq(one(in1(or1(h))),true,one(out1(or1(h))),true),
inference(step,[status(thm)],[t368,t87]) ).
cnf(f31,axiom,
( connection(in1(X),in1(or1(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_connection_in1_in1or1) ).
fof(f31_nnf,plain,
! [X] :
( connection(in1(X),in1(or1(X)))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X] :
( connection(in1(X),in1(or1(X)))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
( connection(in1(X0),in1(or1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(hi27,axiom,
ifeq(halfadder(X0),true,connection(in1(X0),in1(or1(X0))),true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h8,plain,
connection(in1(h),in1(or1(h))) = true,
inference(hyper_resolution,[status(thm)],[hi27,hi36]) ).
cnf(hi1,axiom,
ifeq(connection(X0,X1),true,ifeq(one(X0),true,one(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f41,hypothesis,
one(in1(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in1_1) ).
fof(f41_nnf,plain,
one(in1(h)),
inference(nnf_transformation,[status(thm)],[f41]) ).
cnf(c41,plain,
one(in1(h)),
inference(cnf_transformation,[status(esa)],[f41_nnf]) ).
cnf(hi37,axiom,
one(in1(h)) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(t19,plain,
one(in1(or1(h))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h8,hi37]) ).
cnf(t248,plain,
one(in1(or1(h))) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t1127,plain,
true = ifeq(true,true,one(out1(or1(h))),true),
inference(step,[status(thm)],[t1126,t248]) ).
cnf(t1128,plain,
true = one(out1(or1(h))),
inference(step,[status(thm)],[t1127,t87]) ).
cnf(t387,plain,
one(out1(or1(h))) = true,
inference(orient,[status(thm)],[t1128]) ).
cnf(t390,plain,
true = ifeq(connection(out1(or1(h)),X1),true,ifeq(true,true,one(X1),true),true),
inference(cp,[status(thm)],[t94,t387]) ).
cnf(t1250,plain,
true = ifeq(connection(out1(or1(h)),X1),true,one(X1),true),
inference(step,[status(thm)],[t390,t87]) ).
cnf(t898,plain,
ifeq(connection(out1(or1(h)),X1),true,one(X1),true) = true,
inference(orient,[status(thm)],[t1250]) ).
cnf(f37,axiom,
( connection(out1(or1(X)),in1(and1(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_connection_out1or1_in1_and1) ).
fof(f37_nnf,plain,
! [X] :
( connection(out1(or1(X)),in1(and1(X)))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [X] :
( connection(out1(or1(X)),in1(and1(X)))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
( connection(out1(or1(X0)),in1(and1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi33,axiom,
ifeq(halfadder(X0),true,connection(out1(or1(X0)),in1(and1(X0))),true) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t35,plain,
connection(out1(or1(h)),in1(and1(h))) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi36]) ).
cnf(t272,plain,
connection(out1(or1(h)),in1(and1(h))) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t899,plain,
true = ifeq(true,true,one(in1(and1(h))),true),
inference(cp,[status(thm)],[t898,t272]) ).
cnf(t1251,plain,
true = one(in1(and1(h))),
inference(step,[status(thm)],[t899,t87]) ).
cnf(t913,plain,
one(in1(and1(h))) = true,
inference(orient,[status(thm)],[t1251]) ).
cnf(t917,plain,
true = or(not(zero(in1(and1(h)))),not(true)),
inference(cp,[status(thm)],[t302,t913]) ).
cnf(t2,plain,
not(true) = false,
introduced(definition) ).
cnf(t363,plain,
not(true) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t1253,plain,
true = or(not(zero(in1(and1(h)))),false),
inference(step,[status(thm)],[t917,t363]) ).
cnf(t1254,plain,
true = not(zero(in1(and1(h)))),
inference(step,[status(thm)],[t1253,t88]) ).
cnf(t932,plain,
not(zero(in1(and1(h)))) = true,
inference(orient,[status(thm)],[t1254]) ).
cnf(t933,plain,
false = ifeq(true,true,zero(in1(and1(h))),false),
inference(cp,[status(thm)],[t335,t932]) ).
cnf(t1255,plain,
false = zero(in1(and1(h))),
inference(step,[status(thm)],[t933,t87]) ).
cnf(t934,plain,
zero(in1(and1(h))) = false,
inference(orient,[status(thm)],[t1255]) ).
cnf(t958,plain,
true = ifeq(and_ok(and1(h)),true,ifeq(zero(out1(and1(h))),true,or(false,zero(in2(and1(h)))),true),true),
inference(cp,[status(thm)],[t112,t934]) ).
cnf(f12,axiom,
( abnormal(K)
| and_ok(K)
| ~ logic_and(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_ok_or_abnormal) ).
fof(f12_nnf,plain,
! [K] :
( abnormal(K)
| and_ok(K)
| ~ logic_and(K) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [K] :
( abnormal(K)
| and_ok(K)
| ~ logic_and(K) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( abnormal(X0)
| and_ok(X0)
| ~ logic_and(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t51,plain,
ifeq(logic_and(X1),true,or(and_ok(X1),abnormal(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t139,plain,
ifeq(logic_and(X1),true,or(and_ok(X1),abnormal(X1)),true) = true,
inference(orient,[status(thm)],[t51]) ).
cnf(f45,negated_conjecture,
~ abnormal(and1(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_and1) ).
fof(f45_nnf,plain,
~ abnormal(and1(h)),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
~ abnormal(and1(h)),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
~ abnormal(and1(h)),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(t3,plain,
abnormal(and1(h)) = false,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t345,plain,
abnormal(and1(h)) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t348,plain,
true = ifeq(logic_and(and1(h)),true,or(and_ok(and1(h)),false),true),
inference(cp,[status(thm)],[t139,t345]) ).
cnf(f27,axiom,
( logic_and(and1(X))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_and1) ).
fof(f27_nnf,plain,
! [X] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( logic_and(and1(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi23,axiom,
ifeq(halfadder(X0),true,logic_and(and1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t6,plain,
logic_and(and1(h)) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi36]) ).
cnf(t332,plain,
logic_and(and1(h)) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t1120,plain,
true = ifeq(true,true,or(and_ok(and1(h)),false),true),
inference(step,[status(thm)],[t348,t332]) ).
cnf(t1121,plain,
true = or(and_ok(and1(h)),false),
inference(step,[status(thm)],[t1120,t87]) ).
cnf(t1122,plain,
true = and_ok(and1(h)),
inference(step,[status(thm)],[t1121,t88]) ).
cnf(t373,plain,
and_ok(and1(h)) = true,
inference(orient,[status(thm)],[t1122]) ).
cnf(t1259,plain,
true = ifeq(true,true,ifeq(zero(out1(and1(h))),true,or(false,zero(in2(and1(h)))),true),true),
inference(step,[status(thm)],[t958,t373]) ).
cnf(t1260,plain,
true = ifeq(zero(out1(and1(h))),true,or(false,zero(in2(and1(h)))),true),
inference(step,[status(thm)],[t1259,t87]) ).
cnf(f35,axiom,
( connection(outs(X),out1(and1(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halfadder_connection_outs_out1and1) ).
fof(f35_nnf,plain,
! [X] :
( connection(outs(X),out1(and1(X)))
| ~ halfadder(X) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [X] :
( connection(outs(X),out1(and1(X)))
| ~ halfadder(X) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
( connection(outs(X0),out1(and1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi31,axiom,
ifeq(halfadder(X0),true,connection(outs(X0),out1(and1(X0))),true) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(h4,plain,
connection(outs(h),out1(and1(h))) = true,
inference(hyper_resolution,[status(thm)],[hi31,hi36]) ).
cnf(f43,hypothesis,
zero(outs(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outs_0) ).
fof(f43_nnf,plain,
zero(outs(h)),
inference(nnf_transformation,[status(thm)],[f43]) ).
cnf(c43,plain,
zero(outs(h)),
inference(cnf_transformation,[status(esa)],[f43_nnf]) ).
cnf(hi39,axiom,
zero(outs(h)) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t23,plain,
zero(out1(and1(h))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4,hi39]) ).
cnf(t168,plain,
zero(out1(and1(h))) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t1261,plain,
true = ifeq(true,true,or(false,zero(in2(and1(h)))),true),
inference(step,[status(thm)],[t1260,t168]) ).
cnf(t1262,plain,
true = or(false,zero(in2(and1(h)))),
inference(step,[status(thm)],[t1261,t87]) ).
cnf(t13,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t89,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t1263,plain,
true = zero(in2(and1(h))),
inference(step,[status(thm)],[t1262,t89]) ).
cnf(t962,plain,
zero(in2(and1(h))) = true,
inference(orient,[status(thm)],[t1263]) ).
cnf(t970,plain,
true = or(not(true),not(one(in2(and1(h))))),
inference(cp,[status(thm)],[t302,t962]) ).
cnf(t1265,plain,
true = or(false,not(one(in2(and1(h))))),
inference(step,[status(thm)],[t970,t363]) ).
cnf(t1266,plain,
true = not(one(in2(and1(h)))),
inference(step,[status(thm)],[t1265,t89]) ).
cnf(t988,plain,
not(one(in2(and1(h)))) = true,
inference(orient,[status(thm)],[t1266]) ).
cnf(t989,plain,
false = ifeq(true,true,one(in2(and1(h))),false),
inference(cp,[status(thm)],[t335,t988]) ).
cnf(t1267,plain,
false = one(in2(and1(h))),
inference(step,[status(thm)],[t989,t87]) ).
cnf(t990,plain,
one(in2(and1(h))) = false,
inference(orient,[status(thm)],[t1267]) ).
cnf(t1278,plain,
true = false,
inference(step,[status(thm)],[t1277,t990]) ).
cnf(t1055,plain,
false = true,
inference(orient,[status(thm)],[t1278]) ).
cnf(f11,axiom,
( ~ abnormal(K)
| ~ and_ok(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_and_ok_and_abnormal) ).
fof(f11_nnf,plain,
! [K] :
( ~ abnormal(K)
| ~ and_ok(K) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [K] :
( ~ abnormal(K)
| ~ and_ok(K) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ abnormal(X0)
| ~ and_ok(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(f19,axiom,
( ~ abnormal(K)
| ~ or_ok(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_or_ok_and_abnormal) ).
fof(f19_nnf,plain,
! [K] :
( ~ abnormal(K)
| ~ or_ok(K) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [K] :
( ~ abnormal(K)
| ~ or_ok(K) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ abnormal(X0)
| ~ or_ok(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(f25,axiom,
( ~ abnormal(K)
| ~ not_ok(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not__not_ok_and_abnormal) ).
fof(f25_nnf,plain,
! [K] :
( ~ abnormal(K)
| ~ not_ok(K) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [K] :
( ~ abnormal(K)
| ~ not_ok(K) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( ~ abnormal(X0)
| ~ not_ok(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c11,c19,c25,c45,c46,c47]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1055]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HWV005-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.62 % Computer : n026.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Wed Sep 23 16:22:53 UTC 2026
% 0.15/0.62 % CPUTime :
% 0.15/0.62 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.28/1.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.28/1.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------