%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO635+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 : n011.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 01:18:21 PM UTC 2026
% Result : Theorem 148.69s 19.45s
% Output : Proof 148.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 26
% Syntax : Number of formulae : 272 ( 172 unt; 0 def)
% Number of atoms : 436 ( 168 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 275 ( 111 ~; 105 |; 33 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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; 10 con; 0-4 aty)
% Number of variables : 824 ( 32 sgn 378 !; 11 ?)
% 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(t155,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)],[t155]) ).
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(t82,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)],[t82]) ).
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(t142,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)],[t142]) ).
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(t71,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)],[t71]) ).
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(t214,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)],[t214]) ).
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(t101,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(t311,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t101]) ).
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(t147,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(t305,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)],[t147]) ).
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(t102,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(t294,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t102]) ).
fof(f46,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD46) ).
fof(f46_nnf,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [O,A,B] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
( eqangle(X2,X0,X0,X1,X0,X1,X2,X1)
| ~ cong(X2,X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(t96,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t337,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(orient,[status(thm)],[t96]) ).
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]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,NWPNT1,NWPNT2] :
( ( coll(G,C,E)
& circle(D,C,G,NWPNT2)
& eqangle(A,C,C,E,F,C,C,B)
& circle(D,A,F,NWPNT1)
& coll(E,A,B)
& circle(D,A,B,C) )
=> para(A,B,G,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL8110998) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,NWPNT1,NWPNT2] :
( ( coll(G,C,E)
& circle(D,C,G,NWPNT2)
& eqangle(A,C,C,E,F,C,C,B)
& circle(D,A,F,NWPNT1)
& coll(E,A,B)
& circle(D,A,B,C) )
=> para(A,B,G,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,NWPNT1,NWPNT2] :
( ~ para(A,B,G,F)
& coll(G,C,E)
& circle(D,C,G,NWPNT2)
& eqangle(A,C,C,E,F,C,C,B)
& circle(D,A,F,NWPNT1)
& coll(E,A,B)
& circle(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk20,sk21,sk26,sk25)
& coll(sk26,sk22,sk24)
& circle(sk23,sk22,sk26,sk28)
& eqangle(sk20,sk22,sk22,sk24,sk25,sk22,sk22,sk21)
& circle(sk23,sk20,sk25,sk27)
& coll(sk24,sk20,sk21)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
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]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h15,plain,
perp(sk20,sk23,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
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(h48,plain,
para(sk11(sk20,sk21,sk22,sk23),sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h0,h15]) ).
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(h117,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,h48]) ).
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(h293,plain,
eqangle(sk11(sk20,sk21,sk22,sk23),sk20,sk11(sk20,sk21,sk22,sk23),sk20,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h117]) ).
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(h116,plain,
coll(sk11(sk20,sk21,sk22,sk23),sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h48]) ).
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(h1021,plain,
cyclic(sk20,sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h293,h116]) ).
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(hi43,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,ifeq(cyclic(X0,X1,X2,X5),true,ifeq(eqangle(X2,X0,X2,X1,X5,X3,X5,X4),true,cong(X0,X1,X3,X4),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t10,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi43,h1021,h1021,h1021,h293]) ).
cnf(t2396,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t2399,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t337,t2396]) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t24]) ).
cnf(t21808,plain,
true = eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t2399,t256]) ).
cnf(t4807,plain,
eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t21808]) ).
cnf(t4809,plain,
true = ifeq(true,true,para(sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t311,t4807]) ).
cnf(t21809,plain,
true = para(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t4809,t256]) ).
cnf(t4830,plain,
para(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t21809]) ).
cnf(t4833,plain,
true = ifeq(true,true,eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),true),
inference(cp,[status(thm)],[t294,t4830]) ).
cnf(t22151,plain,
true = eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),
inference(step,[status(thm)],[t4833,t256]) ).
cnf(t9374,plain,
eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t22151]) ).
cnf(t9378,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t305,t9374]) ).
cnf(t22525,plain,
true = eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),
inference(step,[status(thm)],[t9378,t256]) ).
cnf(t13160,plain,
eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t22525]) ).
cnf(t13161,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t311,t13160]) ).
cnf(t22526,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t13161,t256]) ).
cnf(t13183,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t22526]) ).
cnf(t13199,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,t13183]) ).
cnf(t23437,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)],[t13199,t256]) ).
cnf(t23438,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t23437,t13183]) ).
cnf(t23439,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t23438,t256]) ).
cnf(t21188,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t23439]) ).
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(t133,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)],[t133]) ).
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(t74,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)],[t74]) ).
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(t75,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)],[t75]) ).
cnf(t253,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)],[t253]) ).
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(t100,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)],[t100]) ).
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(t77,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)],[t77]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X4,X5,X6,X7,X0,X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(c116,plain,
eqangle(sk20,sk22,sk22,sk24,sk25,sk22,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
eqangle(sk20,sk22,sk22,sk24,sk25,sk22,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h6,plain,
eqangle(sk25,sk22,sk22,sk21,sk20,sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi116]) ).
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(h29,plain,
eqangle(sk25,sk22,sk22,sk21,sk25,sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi21,h6,hi116]) ).
cnf(hi38,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X2,X3),true,para(X0,X1,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h83,plain,
para(sk25,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi38,h29]) ).
cnf(h200,plain,
coll(sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi66,h83]) ).
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]) ).
cnf(h481,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h200,h200]) ).
cnf(h28,plain,
eqangle(sk20,sk22,sk22,sk24,sk20,sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi116,h6]) ).
cnf(h80,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi38,h28]) ).
cnf(h196,plain,
coll(sk20,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi66,h80]) ).
cnf(h473,plain,
coll(sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h196,h196]) ).
cnf(h1139,plain,
coll(sk20,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h473,h481]) ).
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(h2474,plain,
coll(sk20,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1139]) ).
cnf(h3408,plain,
coll(sk25,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2474,h2474]) ).
cnf(h201,plain,
eqangle(sk25,sk22,V0,V1,sk25,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h83]) ).
cnf(t15,plain,
cyclic(sk22,sk20,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi42,h201,h3408]) ).
cnf(t2607,plain,
cyclic(sk22,sk20,sk25,sk25) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t2608,plain,
true = ifeq(true,true,cyclic(sk22,sk25,sk20,sk25),true),
inference(cp,[status(thm)],[t346,t2607]) ).
cnf(t21735,plain,
true = cyclic(sk22,sk25,sk20,sk25),
inference(step,[status(thm)],[t2608,t256]) ).
cnf(t3561,plain,
cyclic(sk22,sk25,sk20,sk25) = true,
inference(orient,[status(thm)],[t21735]) ).
cnf(t3566,plain,
true = ifeq(true,true,eqangle(sk20,sk22,sk20,sk25,sk25,sk22,sk25,sk25),true),
inference(cp,[status(thm)],[t343,t3561]) ).
cnf(t21973,plain,
true = eqangle(sk20,sk22,sk20,sk25,sk25,sk22,sk25,sk25),
inference(step,[status(thm)],[t3566,t256]) ).
cnf(t7527,plain,
eqangle(sk20,sk22,sk20,sk25,sk25,sk22,sk25,sk25) = true,
inference(orient,[status(thm)],[t21973]) ).
cnf(t7543,plain,
true = ifeq(cyclic(sk22,sk25,sk20,sk22),true,ifeq(cyclic(sk22,sk25,sk20,sk25),true,ifeq(cyclic(sk22,sk25,sk20,sk25),true,ifeq(true,true,cong(sk22,sk25,sk22,sk25),true),true),true),true),
inference(cp,[status(thm)],[t341,t7527]) ).
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(t76,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)],[t76]) ).
cnf(h1143,plain,
coll(sk25,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h481,h473]) ).
cnf(h5,plain,
eqangle(sk20,sk22,sk25,sk22,sk22,sk24,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi20,hi116]) ).
cnf(h25,plain,
eqangle(sk22,sk24,sk22,sk21,sk20,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi19,h5]) ).
cnf(h70,plain,
eqangle(sk20,sk22,sk25,sk22,sk20,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi21,h5,h25]) ).
cnf(h173,plain,
eqangle(sk20,sk22,sk20,sk22,sk25,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi20,h70]) ).
cnf(h478,plain,
eqangle(sk25,sk22,sk25,sk22,sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi19,h173]) ).
cnf(t18,plain,
cyclic(sk22,sk22,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h478,h1143]) ).
cnf(t2645,plain,
cyclic(sk22,sk22,sk25,sk20) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t2646,plain,
true = ifeq(true,true,cyclic(sk22,sk25,sk22,sk20),true),
inference(cp,[status(thm)],[t346,t2645]) ).
cnf(t21738,plain,
true = cyclic(sk22,sk25,sk22,sk20),
inference(step,[status(thm)],[t2646,t256]) ).
cnf(t3615,plain,
cyclic(sk22,sk25,sk22,sk20) = true,
inference(orient,[status(thm)],[t21738]) ).
cnf(t3616,plain,
true = ifeq(true,true,cyclic(sk22,sk25,sk20,sk22),true),
inference(cp,[status(thm)],[t348,t3615]) ).
cnf(t21758,plain,
true = cyclic(sk22,sk25,sk20,sk22),
inference(step,[status(thm)],[t3616,t256]) ).
cnf(t3968,plain,
cyclic(sk22,sk25,sk20,sk22) = true,
inference(orient,[status(thm)],[t21758]) ).
cnf(t21974,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk25,sk20,sk25),true,ifeq(cyclic(sk22,sk25,sk20,sk25),true,ifeq(true,true,cong(sk22,sk25,sk22,sk25),true),true),true),true),
inference(step,[status(thm)],[t7543,t3968]) ).
cnf(t21975,plain,
true = ifeq(cyclic(sk22,sk25,sk20,sk25),true,ifeq(cyclic(sk22,sk25,sk20,sk25),true,ifeq(true,true,cong(sk22,sk25,sk22,sk25),true),true),true),
inference(step,[status(thm)],[t21974,t256]) ).
cnf(t21976,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk25,sk20,sk25),true,ifeq(true,true,cong(sk22,sk25,sk22,sk25),true),true),true),
inference(step,[status(thm)],[t21975,t3561]) ).
cnf(t21977,plain,
true = ifeq(cyclic(sk22,sk25,sk20,sk25),true,ifeq(true,true,cong(sk22,sk25,sk22,sk25),true),true),
inference(step,[status(thm)],[t21976,t256]) ).
cnf(t21978,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk25,sk22,sk25),true),true),
inference(step,[status(thm)],[t21977,t3561]) ).
cnf(t21979,plain,
true = ifeq(true,true,cong(sk22,sk25,sk22,sk25),true),
inference(step,[status(thm)],[t21978,t256]) ).
cnf(t21980,plain,
true = cong(sk22,sk25,sk22,sk25),
inference(step,[status(thm)],[t21979,t256]) ).
cnf(t7544,plain,
cong(sk22,sk25,sk22,sk25) = true,
inference(orient,[status(thm)],[t21980]) ).
cnf(t7547,plain,
true = ifeq(true,true,cong(sk22,sk25,sk25,sk22),true),
inference(cp,[status(thm)],[t323,t7544]) ).
cnf(t21984,plain,
true = cong(sk22,sk25,sk25,sk22),
inference(step,[status(thm)],[t7547,t256]) ).
cnf(t7613,plain,
cong(sk22,sk25,sk25,sk22) = true,
inference(orient,[status(thm)],[t21984]) ).
cnf(t7615,plain,
true = ifeq(true,true,cong(sk25,sk22,sk22,sk25),true),
inference(cp,[status(thm)],[t321,t7613]) ).
cnf(t21985,plain,
true = cong(sk25,sk22,sk22,sk25),
inference(step,[status(thm)],[t7615,t256]) ).
cnf(t7623,plain,
cong(sk25,sk22,sk22,sk25) = true,
inference(orient,[status(thm)],[t21985]) ).
cnf(t7625,plain,
true = ifeq(true,true,cong(sk25,sk22,sk25,sk22),true),
inference(cp,[status(thm)],[t323,t7623]) ).
cnf(t21986,plain,
true = cong(sk25,sk22,sk25,sk22),
inference(step,[status(thm)],[t7625,t256]) ).
cnf(t7632,plain,
cong(sk25,sk22,sk25,sk22) = true,
inference(orient,[status(thm)],[t21986]) ).
cnf(t7641,plain,
true = ifeq(true,true,ifeq(coll(sk25,sk22,sk22),true,midp(sk25,sk22,sk22),true),true),
inference(cp,[status(thm)],[t327,t7632]) ).
cnf(t21987,plain,
true = ifeq(coll(sk25,sk22,sk22),true,midp(sk25,sk22,sk22),true),
inference(step,[status(thm)],[t7641,t256]) ).
cnf(t72,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t295,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t72]) ).
cnf(t2612,plain,
true = ifeq(true,true,eqangle(sk25,sk22,sk25,sk20,sk25,sk22,sk25,sk20),true),
inference(cp,[status(thm)],[t343,t2607]) ).
cnf(t21843,plain,
true = eqangle(sk25,sk22,sk25,sk20,sk25,sk22,sk25,sk20),
inference(step,[status(thm)],[t2612,t256]) ).
cnf(t5424,plain,
eqangle(sk25,sk22,sk25,sk20,sk25,sk22,sk25,sk20) = true,
inference(orient,[status(thm)],[t21843]) ).
cnf(t5425,plain,
true = ifeq(true,true,para(sk25,sk22,sk25,sk22),true),
inference(cp,[status(thm)],[t311,t5424]) ).
cnf(t21844,plain,
true = para(sk25,sk22,sk25,sk22),
inference(step,[status(thm)],[t5425,t256]) ).
cnf(t5441,plain,
para(sk25,sk22,sk25,sk22) = true,
inference(orient,[status(thm)],[t21844]) ).
cnf(t5443,plain,
true = ifeq(true,true,coll(sk25,sk22,sk22),true),
inference(cp,[status(thm)],[t295,t5441]) ).
cnf(t21845,plain,
true = coll(sk25,sk22,sk22),
inference(step,[status(thm)],[t5443,t256]) ).
cnf(t5468,plain,
coll(sk25,sk22,sk22) = true,
inference(orient,[status(thm)],[t21845]) ).
cnf(t21988,plain,
true = ifeq(true,true,midp(sk25,sk22,sk22),true),
inference(step,[status(thm)],[t21987,t5468]) ).
cnf(t21989,plain,
true = midp(sk25,sk22,sk22),
inference(step,[status(thm)],[t21988,t256]) ).
cnf(t7671,plain,
midp(sk25,sk22,sk22) = true,
inference(orient,[status(thm)],[t21989]) ).
cnf(t21189,plain,
true = ifeq(true,true,midp(sk25,X1,X1),true),
inference(cp,[status(thm)],[t21188,t7671]) ).
cnf(t23440,plain,
true = midp(sk25,X1,X1),
inference(step,[status(thm)],[t21189,t256]) ).
cnf(t21192,plain,
midp(sk25,X1,X1) = true,
inference(orient,[status(thm)],[t23440]) ).
cnf(t21193,plain,
true = ifeq(true,true,cong(sk25,X1,sk25,X1),true),
inference(cp,[status(thm)],[t363,t21192]) ).
cnf(t23443,plain,
true = cong(sk25,X1,sk25,X1),
inference(step,[status(thm)],[t21193,t256]) ).
cnf(t21258,plain,
cong(sk25,X1,sk25,X1) = true,
inference(orient,[status(thm)],[t23443]) ).
cnf(t21269,plain,
true = ifeq(true,true,ifeq(cong(sk25,X1,sk25,X1),true,perp(sk25,sk25,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t21258]) ).
cnf(t23447,plain,
true = ifeq(cong(sk25,X1,sk25,X1),true,perp(sk25,sk25,X2,X1),true),
inference(step,[status(thm)],[t21269,t256]) ).
cnf(t23448,plain,
true = ifeq(true,true,perp(sk25,sk25,X2,X1),true),
inference(step,[status(thm)],[t23447,t21258]) ).
cnf(t23449,plain,
true = perp(sk25,sk25,X2,X1),
inference(step,[status(thm)],[t23448,t256]) ).
cnf(t21376,plain,
perp(sk25,sk25,X1,X2) = true,
inference(orient,[status(thm)],[t23449]) ).
cnf(t21377,plain,
true = ifeq(true,true,perp(X1,X2,sk25,sk25),true),
inference(cp,[status(thm)],[t274,t21376]) ).
cnf(t23459,plain,
true = perp(X1,X2,sk25,sk25),
inference(step,[status(thm)],[t21377,t256]) ).
cnf(t21540,plain,
perp(X1,X2,sk25,sk25) = true,
inference(orient,[status(thm)],[t23459]) ).
cnf(t21548,plain,
true = ifeq(true,true,ifeq(perp(sk25,sk25,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t21540]) ).
cnf(t23465,plain,
true = ifeq(perp(sk25,sk25,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t21548,t256]) ).
cnf(t23466,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t23465,t21376]) ).
cnf(t23467,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t23466,t256]) ).
cnf(t21702,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t23467]) ).
cnf(c119,plain,
~ para(sk20,sk21,sk26,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk20,sk21,sk26,sk25) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t21702]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO635+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.63 % Computer : n011.cluster.edu
% 0.18/0.63 % Model : x86_64 x86_64
% 0.18/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.63 % Memory : 8046.5625MB
% 0.18/0.63 % OS : Linux 6.8.0-71-generic
% 0.18/0.63 % CPULimit : 300
% 0.18/0.63 % WCLimit : 300
% 0.18/0.63 % DateTime : Wed Sep 23 12:37:13 UTC 2026
% 0.18/0.64 % CPUTime :
% 0.18/0.64 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 148.69/19.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 148.69/19.45 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------