%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO596+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 01:18:15 PM UTC 2026
% Result : Theorem 141.97s 19.06s
% Output : Proof 141.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 30
% Syntax : Number of formulae : 344 ( 228 unt; 0 def)
% Number of atoms : 532 ( 222 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 317 ( 129 ~; 123 |; 35 &)
% ( 0 <=>; 30 =>; 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 : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 1094 ( 108 sgn 442 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(t242,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t302,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(orient,[status(thm)],[t242]) ).
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(t186,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t303,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t186]) ).
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(t183,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t309,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t183]) ).
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(t164,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)],[t164]) ).
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(t193,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)],[t193]) ).
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(t126,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)],[t126]) ).
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(t180,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)],[t180]) ).
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(t113,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)],[t113]) ).
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(t228,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)],[t228]) ).
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(t163,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)],[t163]) ).
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(t185,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)],[t185]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,NWPNT1] :
( ( coll(G,B,C)
& para(A,E,G,F)
& coll(F,C,E)
& coll(F,A,B)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> eqangle(G,F,F,B,F,C,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416058) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,NWPNT1] :
( ( coll(G,B,C)
& para(A,E,G,F)
& coll(F,C,E)
& coll(F,A,B)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> eqangle(G,F,F,B,F,C,C,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,NWPNT1] :
( ~ eqangle(G,F,F,B,F,C,C,B)
& coll(G,B,C)
& para(A,E,G,F)
& coll(F,C,E)
& coll(F,A,B)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk26,sk25,sk25,sk21,sk25,sk22,sk22,sk21)
& coll(sk26,sk21,sk22)
& para(sk20,sk24,sk26,sk25)
& coll(sk25,sk22,sk24)
& coll(sk25,sk20,sk21)
& circle(sk23,sk20,sk24,sk27)
& 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,
para(sk20,sk24,sk26,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
para(sk20,sk24,sk26,sk25) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h10,plain,
para(sk20,sk24,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi117]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h41,plain,
para(sk25,sk26,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi4,h10]) ).
fof(f5,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD6) ).
fof(f5_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(para(X0,X1,X2,X3),true,ifeq(para(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t38,plain,
para(sk25,sk26,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi5,h41,h10]) ).
cnf(t1879,plain,
para(sk25,sk26,sk25,sk26) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(t1882,plain,
true = ifeq(true,true,eqangle(sk25,sk26,X1,X2,sk25,sk26,X1,X2),true),
inference(cp,[status(thm)],[t294,t1879]) ).
cnf(t31,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t31]) ).
cnf(t31855,plain,
true = eqangle(sk25,sk26,X1,X2,sk25,sk26,X1,X2),
inference(step,[status(thm)],[t1882,t256]) ).
cnf(t7414,plain,
eqangle(sk25,sk26,X1,X2,sk25,sk26,X1,X2) = true,
inference(orient,[status(thm)],[t31855]) ).
cnf(t7421,plain,
true = ifeq(true,true,eqangle(X1,X2,sk25,sk26,X1,X2,sk25,sk26),true),
inference(cp,[status(thm)],[t305,t7414]) ).
cnf(t32307,plain,
true = eqangle(X1,X2,sk25,sk26,X1,X2,sk25,sk26),
inference(step,[status(thm)],[t7421,t256]) ).
cnf(t13120,plain,
eqangle(X1,X2,sk25,sk26,X1,X2,sk25,sk26) = true,
inference(orient,[status(thm)],[t32307]) ).
cnf(t13122,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t311,t13120]) ).
cnf(t32308,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t13122,t256]) ).
cnf(t13144,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t32308]) ).
cnf(t13160,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,t13144]) ).
cnf(t34093,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)],[t13160,t256]) ).
cnf(t34094,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t34093,t13144]) ).
cnf(t34095,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t34094,t256]) ).
cnf(t28995,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t34095]) ).
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(t171,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)],[t171]) ).
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(t118,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)],[t118]) ).
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(t119,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)],[t119]) ).
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(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(t162,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)],[t162]) ).
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(t120,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)],[t120]) ).
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(t121,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)],[t121]) ).
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(c116,plain,
coll(sk25,sk22,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk25,sk22,sk24) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h7,plain,
coll(sk25,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi116]) ).
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(h28,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h7,h7]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c118,plain,
coll(sk26,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk26,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h12,plain,
coll(sk21,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi118]) ).
cnf(h42,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h12,h12]) ).
cnf(h83,plain,
coll(sk21,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h42,h28]) ).
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(h8,plain,
eqangle(sk20,sk24,V0,V1,sk26,sk25,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi117]) ).
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(h32,plain,
eqangle(sk20,sk24,sk26,sk25,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h8]) ).
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(h86,plain,
eqangle(V0,V1,V0,V1,sk20,sk24,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi19,h32]) ).
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(h222,plain,
eqangle(V0,V1,V0,V1,V2,V3,V2,V3) = true,
inference(hyper_resolution,[status(thm)],[hi21,h86,h32]) ).
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(t18,plain,
cyclic(sk22,sk22,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi42,h222,h83]) ).
cnf(t2768,plain,
cyclic(sk22,sk22,sk21,sk25) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t2769,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk22,sk25),true),
inference(cp,[status(thm)],[t346,t2768]) ).
cnf(t31690,plain,
true = cyclic(sk22,sk21,sk22,sk25),
inference(step,[status(thm)],[t2769,t256]) ).
cnf(t4181,plain,
cyclic(sk22,sk21,sk22,sk25) = true,
inference(orient,[status(thm)],[t31690]) ).
cnf(t4182,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk25,sk22),true),
inference(cp,[status(thm)],[t348,t4181]) ).
cnf(t31724,plain,
true = cyclic(sk22,sk21,sk25,sk22),
inference(step,[status(thm)],[t4182,t256]) ).
cnf(t4800,plain,
cyclic(sk22,sk21,sk25,sk22) = true,
inference(orient,[status(thm)],[t31724]) ).
cnf(t4803,plain,
true = ifeq(true,true,eqangle(sk25,sk22,sk25,sk21,sk22,sk22,sk22,sk21),true),
inference(cp,[status(thm)],[t343,t4800]) ).
cnf(t32220,plain,
true = eqangle(sk25,sk22,sk25,sk21,sk22,sk22,sk22,sk21),
inference(step,[status(thm)],[t4803,t256]) ).
cnf(t12131,plain,
eqangle(sk25,sk22,sk25,sk21,sk22,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t32220]) ).
cnf(t12145,plain,
true = ifeq(cyclic(sk22,sk21,sk25,sk22),true,ifeq(cyclic(sk22,sk21,sk25,sk21),true,ifeq(cyclic(sk22,sk21,sk25,sk22),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),true),true),
inference(cp,[status(thm)],[t341,t12131]) ).
cnf(t32221,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk21,sk25,sk21),true,ifeq(cyclic(sk22,sk21,sk25,sk22),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),true),true),
inference(step,[status(thm)],[t12145,t4800]) ).
cnf(t32222,plain,
true = ifeq(cyclic(sk22,sk21,sk25,sk21),true,ifeq(cyclic(sk22,sk21,sk25,sk22),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),true),
inference(step,[status(thm)],[t32221,t256]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t122,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t344,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t122]) ).
cnf(c115,plain,
coll(sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
coll(sk25,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h2,plain,
coll(sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi115,hi115]) ).
cnf(h81,plain,
coll(sk21,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h42,h42]) ).
cnf(h209,plain,
coll(sk22,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h81,h2]) ).
cnf(t13,plain,
cyclic(sk21,sk21,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi42,h222,h209]) ).
cnf(t2840,plain,
cyclic(sk21,sk21,sk22,sk25) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t2841,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk21,sk25),true),
inference(cp,[status(thm)],[t346,t2840]) ).
cnf(t31694,plain,
true = cyclic(sk21,sk22,sk21,sk25),
inference(step,[status(thm)],[t2841,t256]) ).
cnf(t4257,plain,
cyclic(sk21,sk22,sk21,sk25) = true,
inference(orient,[status(thm)],[t31694]) ).
cnf(t4258,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk25,sk21),true),
inference(cp,[status(thm)],[t348,t4257]) ).
cnf(t31732,plain,
true = cyclic(sk21,sk22,sk25,sk21),
inference(step,[status(thm)],[t4258,t256]) ).
cnf(t4940,plain,
cyclic(sk21,sk22,sk25,sk21) = true,
inference(orient,[status(thm)],[t31732]) ).
cnf(t4941,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk25,sk21),true),
inference(cp,[status(thm)],[t344,t4940]) ).
cnf(t31756,plain,
true = cyclic(sk22,sk21,sk25,sk21),
inference(step,[status(thm)],[t4941,t256]) ).
cnf(t5373,plain,
cyclic(sk22,sk21,sk25,sk21) = true,
inference(orient,[status(thm)],[t31756]) ).
cnf(t32223,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk21,sk25,sk22),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),true),
inference(step,[status(thm)],[t32222,t5373]) ).
cnf(t32224,plain,
true = ifeq(cyclic(sk22,sk21,sk25,sk22),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),
inference(step,[status(thm)],[t32223,t256]) ).
cnf(t32225,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),
inference(step,[status(thm)],[t32224,t4800]) ).
cnf(t32226,plain,
true = ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),
inference(step,[status(thm)],[t32225,t256]) ).
cnf(t32227,plain,
true = cong(sk22,sk21,sk22,sk21),
inference(step,[status(thm)],[t32226,t256]) ).
cnf(t12146,plain,
cong(sk22,sk21,sk22,sk21) = true,
inference(orient,[status(thm)],[t32227]) ).
cnf(t12149,plain,
true = ifeq(true,true,cong(sk22,sk21,sk21,sk22),true),
inference(cp,[status(thm)],[t323,t12146]) ).
cnf(t32231,plain,
true = cong(sk22,sk21,sk21,sk22),
inference(step,[status(thm)],[t12149,t256]) ).
cnf(t12214,plain,
cong(sk22,sk21,sk21,sk22) = true,
inference(orient,[status(thm)],[t32231]) ).
cnf(t12216,plain,
true = ifeq(true,true,cong(sk21,sk22,sk22,sk21),true),
inference(cp,[status(thm)],[t321,t12214]) ).
cnf(t32232,plain,
true = cong(sk21,sk22,sk22,sk21),
inference(step,[status(thm)],[t12216,t256]) ).
cnf(t12224,plain,
cong(sk21,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t32232]) ).
cnf(t12226,plain,
true = ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t323,t12224]) ).
cnf(t32233,plain,
true = cong(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t12226,t256]) ).
cnf(t12233,plain,
cong(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t32233]) ).
cnf(t12242,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),true),
inference(cp,[status(thm)],[t327,t12233]) ).
cnf(t32234,plain,
true = ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t12242,t256]) ).
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(t114,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)],[t114]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t212,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t299,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t212]) ).
cnf(t2771,plain,
true = ifeq(true,true,eqangle(sk21,sk22,sk21,sk22,sk25,sk22,sk25,sk22),true),
inference(cp,[status(thm)],[t343,t2768]) ).
cnf(t31952,plain,
true = eqangle(sk21,sk22,sk21,sk22,sk25,sk22,sk25,sk22),
inference(step,[status(thm)],[t2771,t256]) ).
cnf(t8919,plain,
eqangle(sk21,sk22,sk21,sk22,sk25,sk22,sk25,sk22) = true,
inference(orient,[status(thm)],[t31952]) ).
cnf(t8928,plain,
true = ifeq(true,true,ifeq(para(sk25,sk22,sk25,sk22),true,para(sk21,sk22,sk21,sk22),true),true),
inference(cp,[status(thm)],[t299,t8919]) ).
cnf(t31953,plain,
true = ifeq(para(sk25,sk22,sk25,sk22),true,para(sk21,sk22,sk21,sk22),true),
inference(step,[status(thm)],[t8928,t256]) ).
cnf(h11,plain,
coll(sk22,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi118,hi118]) ).
cnf(h75,plain,
coll(sk25,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h28,h11]) ).
cnf(t20,plain,
cyclic(sk22,sk22,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi42,h222,h75]) ).
cnf(t2713,plain,
cyclic(sk22,sk22,sk25,sk26) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t2718,plain,
true = ifeq(true,true,eqangle(sk25,sk22,sk25,sk22,sk26,sk22,sk26,sk22),true),
inference(cp,[status(thm)],[t343,t2713]) ).
cnf(t31931,plain,
true = eqangle(sk25,sk22,sk25,sk22,sk26,sk22,sk26,sk22),
inference(step,[status(thm)],[t2718,t256]) ).
cnf(t8587,plain,
eqangle(sk25,sk22,sk25,sk22,sk26,sk22,sk26,sk22) = true,
inference(orient,[status(thm)],[t31931]) ).
cnf(t8598,plain,
true = ifeq(true,true,ifeq(para(sk26,sk22,sk26,sk22),true,para(sk25,sk22,sk25,sk22),true),true),
inference(cp,[status(thm)],[t299,t8587]) ).
cnf(t31932,plain,
true = ifeq(para(sk26,sk22,sk26,sk22),true,para(sk25,sk22,sk25,sk22),true),
inference(step,[status(thm)],[t8598,t256]) ).
cnf(t123,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t292,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t123]) ).
cnf(t124,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t290,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t124]) ).
cnf(h9,plain,
para(sk26,sk25,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi117]) ).
cnf(h37,plain,
para(sk26,sk25,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi5,h9,hi117]) ).
cnf(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h110,plain,
coll(sk26,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi66,h37]) ).
cnf(h74,plain,
coll(sk26,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h11,h28]) ).
cnf(h289,plain,
coll(sk22,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h74,h110]) ).
cnf(t29,plain,
cyclic(sk26,sk26,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi42,h222,h289]) ).
cnf(t2660,plain,
cyclic(sk26,sk26,sk22,sk25) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t2663,plain,
true = ifeq(true,true,eqangle(sk22,sk26,sk22,sk26,sk25,sk26,sk25,sk26),true),
inference(cp,[status(thm)],[t343,t2660]) ).
cnf(t31902,plain,
true = eqangle(sk22,sk26,sk22,sk26,sk25,sk26,sk25,sk26),
inference(step,[status(thm)],[t2663,t256]) ).
cnf(t7972,plain,
eqangle(sk22,sk26,sk22,sk26,sk25,sk26,sk25,sk26) = true,
inference(orient,[status(thm)],[t31902]) ).
cnf(t7981,plain,
true = ifeq(true,true,ifeq(para(sk25,sk26,sk25,sk26),true,para(sk22,sk26,sk22,sk26),true),true),
inference(cp,[status(thm)],[t299,t7972]) ).
cnf(t31903,plain,
true = ifeq(para(sk25,sk26,sk25,sk26),true,para(sk22,sk26,sk22,sk26),true),
inference(step,[status(thm)],[t7981,t256]) ).
cnf(t31904,plain,
true = ifeq(true,true,para(sk22,sk26,sk22,sk26),true),
inference(step,[status(thm)],[t31903,t1879]) ).
cnf(t31905,plain,
true = para(sk22,sk26,sk22,sk26),
inference(step,[status(thm)],[t31904,t256]) ).
cnf(t7986,plain,
para(sk22,sk26,sk22,sk26) = true,
inference(orient,[status(thm)],[t31905]) ).
cnf(t7989,plain,
true = ifeq(true,true,para(sk22,sk26,sk26,sk22),true),
inference(cp,[status(thm)],[t292,t7986]) ).
cnf(t31909,plain,
true = para(sk22,sk26,sk26,sk22),
inference(step,[status(thm)],[t7989,t256]) ).
cnf(t8103,plain,
para(sk22,sk26,sk26,sk22) = true,
inference(orient,[status(thm)],[t31909]) ).
cnf(t8106,plain,
true = ifeq(true,true,para(sk26,sk22,sk22,sk26),true),
inference(cp,[status(thm)],[t290,t8103]) ).
cnf(t31910,plain,
true = para(sk26,sk22,sk22,sk26),
inference(step,[status(thm)],[t8106,t256]) ).
cnf(t8128,plain,
para(sk26,sk22,sk22,sk26) = true,
inference(orient,[status(thm)],[t31910]) ).
cnf(t8131,plain,
true = ifeq(true,true,para(sk26,sk22,sk26,sk22),true),
inference(cp,[status(thm)],[t292,t8128]) ).
cnf(t31911,plain,
true = para(sk26,sk22,sk26,sk22),
inference(step,[status(thm)],[t8131,t256]) ).
cnf(t8152,plain,
para(sk26,sk22,sk26,sk22) = true,
inference(orient,[status(thm)],[t31911]) ).
cnf(t31933,plain,
true = ifeq(true,true,para(sk25,sk22,sk25,sk22),true),
inference(step,[status(thm)],[t31932,t8152]) ).
cnf(t31934,plain,
true = para(sk25,sk22,sk25,sk22),
inference(step,[status(thm)],[t31933,t256]) ).
cnf(t8603,plain,
para(sk25,sk22,sk25,sk22) = true,
inference(orient,[status(thm)],[t31934]) ).
cnf(t31954,plain,
true = ifeq(true,true,para(sk21,sk22,sk21,sk22),true),
inference(step,[status(thm)],[t31953,t8603]) ).
cnf(t31955,plain,
true = para(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t31954,t256]) ).
cnf(t8933,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t31955]) ).
cnf(t8934,plain,
true = ifeq(true,true,coll(sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t295,t8933]) ).
cnf(t31956,plain,
true = coll(sk21,sk22,sk22),
inference(step,[status(thm)],[t8934,t256]) ).
cnf(t8959,plain,
coll(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t31956]) ).
cnf(t32235,plain,
true = ifeq(true,true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t32234,t8959]) ).
cnf(t32236,plain,
true = midp(sk21,sk22,sk22),
inference(step,[status(thm)],[t32235,t256]) ).
cnf(t12272,plain,
midp(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t32236]) ).
cnf(t28996,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t28995,t12272]) ).
cnf(t34096,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t28996,t256]) ).
cnf(t29010,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t34096]) ).
cnf(t29011,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t363,t29010]) ).
cnf(t34101,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t29011,t256]) ).
cnf(t29110,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t34101]) ).
cnf(t29121,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t29110]) ).
cnf(t34107,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t29121,t256]) ).
cnf(t34108,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t34107,t29110]) ).
cnf(t34109,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t34108,t256]) ).
cnf(t29291,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t34109]) ).
cnf(t29294,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t274,t29291]) ).
cnf(t34136,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t29294,t256]) ).
cnf(t29594,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t34136]) ).
cnf(t29608,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t29594]) ).
cnf(t34154,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t29608,t256]) ).
cnf(t34155,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t34154,t29291]) ).
cnf(t34156,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t34155,t256]) ).
cnf(t29985,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t34156]) ).
cnf(t34162,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t294,t29985]) ).
cnf(t34163,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t34162,t256]) ).
cnf(t29990,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t34163]) ).
cnf(t30726,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t29990]) ).
cnf(t30729,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t309,t30726]) ).
cnf(t34270,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t30729,t256]) ).
cnf(t30946,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t34270]) ).
cnf(t30948,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t303,t30946]) ).
cnf(t34307,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t30948,t256]) ).
cnf(t31455,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t34307]) ).
cnf(t31466,plain,
true = ifeq(eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(cp,[status(thm)],[t302,t31455]) ).
cnf(t34361,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t31466,t30946]) ).
cnf(t34362,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t34361,t256]) ).
cnf(t34363,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t34362,t256]) ).
cnf(t31646,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t34363]) ).
cnf(c119,plain,
~ eqangle(sk26,sk25,sk25,sk21,sk25,sk22,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk26,sk25,sk25,sk21,sk25,sk22,sk22,sk21) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t31646]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO596+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 12:30:12 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 141.97/19.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 141.97/19.06 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------