%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO589+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:18:14 PM UTC 2026
% Result : Theorem 86.18s 11.52s
% Output : Proof 86.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 25
% Syntax : Number of formulae : 266 ( 170 unt; 0 def)
% Number of atoms : 429 ( 165 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 274 ( 111 ~; 105 |; 33 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-5 aty)
% Number of variables : 790 ( 32 sgn 358 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t131,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t265,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t131]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t57,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t274,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t57]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t118,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t326,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t118]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t45,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t363,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t45]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t207,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t353,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t207]) ).
fof(f38,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t80,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t296,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t80]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t123,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t290,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t123]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(t81,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t312,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t81]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f94,conjecture,
! [A,B,C,O,D,E,NWPNT1,NWPNT2] :
( ( coll(E,D,O)
& circle(O,D,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) )
=> para(B,E,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416051) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,NWPNT1,NWPNT2] :
( ( coll(E,D,O)
& circle(O,D,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) )
=> para(B,E,A,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,E,NWPNT1,NWPNT2] :
( ~ para(B,E,A,C)
& coll(E,D,O)
& circle(O,D,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk21,sk25,sk20,sk22)
& coll(sk25,sk24,sk23)
& circle(sk23,sk24,sk25,sk27)
& circle(sk23,sk20,sk24,sk26)
& perp(sk20,sk22,sk21,sk24)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c117,plain,
coll(sk25,sk24,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk24,sk23) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h5,plain,
coll(sk23,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
fof(f86,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX11) ).
fof(f86_nnf,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [O,A,B,C] :
( perp(sk11(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f86_nnf]) ).
cnf(c99,plain,
( perp(sk11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(hi99,axiom,
ifeq(circle(X0,X1,X2,X3),true,perp(sk11(X1,X2,X3,X0),X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
cnf(c113,plain,
circle(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
circle(sk23,sk20,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk11(sk20,sk21,sk22,sk23),sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi113]) ).
fof(f90,axiom,
! [A,B,C,E,F] :
? [P] :
( ( coll(B,E,F)
& perp(A,C,C,B) )
=> ( perp(P,A,E,F)
& coll(P,E,F) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX15) ).
fof(f90_nnf,plain,
! [A,B,C,E,F] :
? [P] :
( ( perp(P,A,E,F)
& coll(P,E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(nnf_transformation,[status(thm)],[f90]) ).
fof(f90_sk,plain,
! [A,C,B,E,F] :
( ( perp(sk16(A,B,C,E,F),A,E,F)
& coll(sk16(A,B,C,E,F),E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f90_nnf]) ).
cnf(c107,plain,
( perp(sk16(X0,X1,X2,X3,X4),X0,X3,X4)
| ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f90_sk]) ).
cnf(hi107,axiom,
ifeq(perp(X0,X1,X1,X2),true,ifeq(coll(X2,X3,X4),true,perp(sk16(X0,X2,X1,X3,X4),X0,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(h10,plain,
perp(sk16(sk11(sk20,sk21,sk22,sk23),sk23,sk20,sk23,sk25),sk11(sk20,sk21,sk22,sk23),sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi107,h0,h5]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h38,plain,
perp(sk23,sk25,sk16(sk11(sk20,sk21,sk22,sk23),sk23,sk20,sk23,sk25),sk11(sk20,sk21,sk22,sk23)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h10]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h135,plain,
para(sk23,sk25,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,h38,h10]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h586,plain,
eqangle(sk23,sk25,V0,V1,sk23,sk25,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h135]) ).
cnf(h8,plain,
perp(sk20,sk23,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(h32,plain,
para(sk11(sk20,sk21,sk22,sk23),sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h0,h8]) ).
cnf(h101,plain,
eqangle(sk11(sk20,sk21,sk22,sk23),sk20,V0,V1,sk11(sk20,sk21,sk22,sk23),sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h32]) ).
cnf(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h384,plain,
eqangle(V0,V1,sk11(sk20,sk21,sk22,sk23),sk20,V0,V1,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,h101]) ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t70,plain,
eqangle(sk23,sk25,sk11(sk20,sk21,sk22,sk23),sk20,sk23,sk25,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi21,h384,h586]) ).
cnf(t1556,plain,
eqangle(sk23,sk25,sk11(sk20,sk21,sk22,sk23),sk20,sk23,sk25,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(orient,[status(thm)],[t70]) ).
cnf(t1558,plain,
true = ifeq(true,true,para(sk23,sk25,sk23,sk25),true),
inference(cp,[status(thm)],[t296,t1556]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t12340,plain,
true = para(sk23,sk25,sk23,sk25),
inference(step,[status(thm)],[t1558,t256]) ).
cnf(t3182,plain,
para(sk23,sk25,sk23,sk25) = true,
inference(orient,[status(thm)],[t12340]) ).
cnf(t3186,plain,
true = ifeq(true,true,eqangle(sk23,sk25,X1,X2,sk23,sk25,X1,X2),true),
inference(cp,[status(thm)],[t312,t3182]) ).
cnf(t12444,plain,
true = eqangle(sk23,sk25,X1,X2,sk23,sk25,X1,X2),
inference(step,[status(thm)],[t3186,t256]) ).
cnf(t5210,plain,
eqangle(sk23,sk25,X1,X2,sk23,sk25,X1,X2) = true,
inference(orient,[status(thm)],[t12444]) ).
cnf(t5217,plain,
true = ifeq(true,true,eqangle(X1,X2,sk23,sk25,X1,X2,sk23,sk25),true),
inference(cp,[status(thm)],[t290,t5210]) ).
cnf(t12619,plain,
true = eqangle(X1,X2,sk23,sk25,X1,X2,sk23,sk25),
inference(step,[status(thm)],[t5217,t256]) ).
cnf(t8125,plain,
eqangle(X1,X2,sk23,sk25,X1,X2,sk23,sk25) = true,
inference(orient,[status(thm)],[t12619]) ).
cnf(t8128,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t8125]) ).
cnf(t12620,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t8128,t256]) ).
cnf(t8150,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t12620]) ).
cnf(t8166,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t353,t8150]) ).
cnf(t13114,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t8166,t256]) ).
cnf(t13115,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t13114,t8150]) ).
cnf(t13116,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t13115,t256]) ).
cnf(t11990,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t13116]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t107,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t327,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t107]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t49,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t323,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t49]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t50,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t321,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t50]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t245,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t341,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t245]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t79,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t343,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t79]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t52,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t346,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(h33,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,h8,h0]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h107,plain,
coll(sk20,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi66,h33]) ).
cnf(h302,plain,
coll(sk23,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h107,h107]) ).
cnf(h490,plain,
coll(sk25,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5,h302]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h864,plain,
coll(sk25,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h490]) ).
cnf(h1410,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h864,h864]) ).
cnf(c114,plain,
perp(sk20,sk22,sk21,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
perp(sk20,sk22,sk21,sk24) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h1,plain,
perp(sk21,sk24,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi114]) ).
cnf(h14,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi114,h1]) ).
cnf(h52,plain,
eqangle(sk20,sk22,V0,V1,sk20,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h14]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(t16,plain,
cyclic(sk22,sk25,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h52,h1410]) ).
cnf(t2516,plain,
cyclic(sk22,sk25,sk20,sk20) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t2517,plain,
true = ifeq(true,true,cyclic(sk22,sk20,sk25,sk20),true),
inference(cp,[status(thm)],[t346,t2516]) ).
cnf(t12352,plain,
true = cyclic(sk22,sk20,sk25,sk20),
inference(step,[status(thm)],[t2517,t256]) ).
cnf(t3431,plain,
cyclic(sk22,sk20,sk25,sk20) = true,
inference(orient,[status(thm)],[t12352]) ).
cnf(t3436,plain,
true = ifeq(true,true,eqangle(sk25,sk22,sk25,sk20,sk20,sk22,sk20,sk20),true),
inference(cp,[status(thm)],[t343,t3431]) ).
cnf(t12482,plain,
true = eqangle(sk25,sk22,sk25,sk20,sk20,sk22,sk20,sk20),
inference(step,[status(thm)],[t3436,t256]) ).
cnf(t5900,plain,
eqangle(sk25,sk22,sk25,sk20,sk20,sk22,sk20,sk20) = true,
inference(orient,[status(thm)],[t12482]) ).
cnf(t5916,plain,
true = ifeq(cyclic(sk22,sk20,sk25,sk22),true,ifeq(cyclic(sk22,sk20,sk25,sk20),true,ifeq(cyclic(sk22,sk20,sk25,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),true),true),
inference(cp,[status(thm)],[t341,t5900]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t51,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t348,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t51]) ).
cnf(h51,plain,
coll(sk20,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi66,h14]) ).
cnf(h150,plain,
coll(sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h51,h51]) ).
cnf(h313,plain,
coll(sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h150,h150]) ).
cnf(h2430,plain,
coll(sk22,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h313,h1410]) ).
cnf(h4078,plain,
coll(sk22,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2430]) ).
cnf(h534,plain,
coll(sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h313]) ).
cnf(h988,plain,
coll(sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h51,h534]) ).
cnf(h5098,plain,
coll(sk20,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h988,h4078]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD21) ).
fof(f20_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi20,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X0,X1,X4,X5,X2,X3,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h176,plain,
eqangle(sk20,sk22,sk20,sk22,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h52]) ).
cnf(t15,plain,
cyclic(sk22,sk22,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi42,h176,h5098]) ).
cnf(t2478,plain,
cyclic(sk22,sk22,sk20,sk25) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t2481,plain,
true = ifeq(true,true,cyclic(sk22,sk20,sk22,sk25),true),
inference(cp,[status(thm)],[t346,t2478]) ).
cnf(t12349,plain,
true = cyclic(sk22,sk20,sk22,sk25),
inference(step,[status(thm)],[t2481,t256]) ).
cnf(t3376,plain,
cyclic(sk22,sk20,sk22,sk25) = true,
inference(orient,[status(thm)],[t12349]) ).
cnf(t3377,plain,
true = ifeq(true,true,cyclic(sk22,sk20,sk25,sk22),true),
inference(cp,[status(thm)],[t348,t3376]) ).
cnf(t12360,plain,
true = cyclic(sk22,sk20,sk25,sk22),
inference(step,[status(thm)],[t3377,t256]) ).
cnf(t3597,plain,
cyclic(sk22,sk20,sk25,sk22) = true,
inference(orient,[status(thm)],[t12360]) ).
cnf(t12483,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk20,sk25,sk20),true,ifeq(cyclic(sk22,sk20,sk25,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),true),true),
inference(step,[status(thm)],[t5916,t3597]) ).
cnf(t12484,plain,
true = ifeq(cyclic(sk22,sk20,sk25,sk20),true,ifeq(cyclic(sk22,sk20,sk25,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),true),
inference(step,[status(thm)],[t12483,t256]) ).
cnf(t12485,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk20,sk25,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),true),
inference(step,[status(thm)],[t12484,t3431]) ).
cnf(t12486,plain,
true = ifeq(cyclic(sk22,sk20,sk25,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),
inference(step,[status(thm)],[t12485,t256]) ).
cnf(t12487,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),
inference(step,[status(thm)],[t12486,t3431]) ).
cnf(t12488,plain,
true = ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),
inference(step,[status(thm)],[t12487,t256]) ).
cnf(t12489,plain,
true = cong(sk22,sk20,sk22,sk20),
inference(step,[status(thm)],[t12488,t256]) ).
cnf(t5917,plain,
cong(sk22,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t12489]) ).
cnf(t5920,plain,
true = ifeq(true,true,cong(sk22,sk20,sk20,sk22),true),
inference(cp,[status(thm)],[t323,t5917]) ).
cnf(t12493,plain,
true = cong(sk22,sk20,sk20,sk22),
inference(step,[status(thm)],[t5920,t256]) ).
cnf(t5985,plain,
cong(sk22,sk20,sk20,sk22) = true,
inference(orient,[status(thm)],[t12493]) ).
cnf(t5987,plain,
true = ifeq(true,true,cong(sk20,sk22,sk22,sk20),true),
inference(cp,[status(thm)],[t321,t5985]) ).
cnf(t12494,plain,
true = cong(sk20,sk22,sk22,sk20),
inference(step,[status(thm)],[t5987,t256]) ).
cnf(t5995,plain,
cong(sk20,sk22,sk22,sk20) = true,
inference(orient,[status(thm)],[t12494]) ).
cnf(t5997,plain,
true = ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),
inference(cp,[status(thm)],[t323,t5995]) ).
cnf(t12495,plain,
true = cong(sk20,sk22,sk20,sk22),
inference(step,[status(thm)],[t5997,t256]) ).
cnf(t6004,plain,
cong(sk20,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t12495]) ).
cnf(t6013,plain,
true = ifeq(true,true,ifeq(coll(sk20,sk22,sk22),true,midp(sk20,sk22,sk22),true),true),
inference(cp,[status(thm)],[t327,t6004]) ).
cnf(t12496,plain,
true = ifeq(coll(sk20,sk22,sk22),true,midp(sk20,sk22,sk22),true),
inference(step,[status(thm)],[t6013,t256]) ).
cnf(t46,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t319,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(t2521,plain,
true = ifeq(true,true,eqangle(sk20,sk22,sk20,sk25,sk20,sk22,sk20,sk25),true),
inference(cp,[status(thm)],[t343,t2516]) ).
cnf(t12425,plain,
true = eqangle(sk20,sk22,sk20,sk25,sk20,sk22,sk20,sk25),
inference(step,[status(thm)],[t2521,t256]) ).
cnf(t4754,plain,
eqangle(sk20,sk22,sk20,sk25,sk20,sk22,sk20,sk25) = true,
inference(orient,[status(thm)],[t12425]) ).
cnf(t4755,plain,
true = ifeq(true,true,para(sk20,sk22,sk20,sk22),true),
inference(cp,[status(thm)],[t296,t4754]) ).
cnf(t12426,plain,
true = para(sk20,sk22,sk20,sk22),
inference(step,[status(thm)],[t4755,t256]) ).
cnf(t4771,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t12426]) ).
cnf(t4772,plain,
true = ifeq(true,true,coll(sk20,sk22,sk22),true),
inference(cp,[status(thm)],[t319,t4771]) ).
cnf(t12427,plain,
true = coll(sk20,sk22,sk22),
inference(step,[status(thm)],[t4772,t256]) ).
cnf(t4798,plain,
coll(sk20,sk22,sk22) = true,
inference(orient,[status(thm)],[t12427]) ).
cnf(t12497,plain,
true = ifeq(true,true,midp(sk20,sk22,sk22),true),
inference(step,[status(thm)],[t12496,t4798]) ).
cnf(t12498,plain,
true = midp(sk20,sk22,sk22),
inference(step,[status(thm)],[t12497,t256]) ).
cnf(t6043,plain,
midp(sk20,sk22,sk22) = true,
inference(orient,[status(thm)],[t12498]) ).
cnf(t11991,plain,
true = ifeq(true,true,midp(sk20,X1,X1),true),
inference(cp,[status(thm)],[t11990,t6043]) ).
cnf(t13117,plain,
true = midp(sk20,X1,X1),
inference(step,[status(thm)],[t11991,t256]) ).
cnf(t11994,plain,
midp(sk20,X1,X1) = true,
inference(orient,[status(thm)],[t13117]) ).
cnf(t11995,plain,
true = ifeq(true,true,cong(sk20,X1,sk20,X1),true),
inference(cp,[status(thm)],[t363,t11994]) ).
cnf(t13119,plain,
true = cong(sk20,X1,sk20,X1),
inference(step,[status(thm)],[t11995,t256]) ).
cnf(t12034,plain,
cong(sk20,X1,sk20,X1) = true,
inference(orient,[status(thm)],[t13119]) ).
cnf(t12045,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t12034]) ).
cnf(t13122,plain,
true = ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t12045,t256]) ).
cnf(t13123,plain,
true = ifeq(true,true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t13122,t12034]) ).
cnf(t13124,plain,
true = perp(sk20,sk20,X2,X1),
inference(step,[status(thm)],[t13123,t256]) ).
cnf(t12122,plain,
perp(sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t13124]) ).
cnf(t12123,plain,
true = ifeq(true,true,perp(X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t274,t12122]) ).
cnf(t13131,plain,
true = perp(X1,X2,sk20,sk20),
inference(step,[status(thm)],[t12123,t256]) ).
cnf(t12221,plain,
perp(X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t13131]) ).
cnf(t12229,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t12221]) ).
cnf(t13135,plain,
true = ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t12229,t256]) ).
cnf(t13136,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t13135,t12122]) ).
cnf(t13137,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t13136,t256]) ).
cnf(t12320,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t13137]) ).
cnf(c118,plain,
~ para(sk21,sk25,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk21,sk25,sk20,sk22) != true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t12320]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO589+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 12:31:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 86.18/11.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 86.18/11.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------