%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO624+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 : n012.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 01:18:19 PM UTC 2026
% Result : Theorem 94.49s 22.62s
% Output : Proof 94.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 30
% Syntax : Number of formulae : 331 ( 215 unt; 0 def)
% Number of atoms : 551 ( 207 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 355 ( 135 ~; 129 |; 61 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-4 aty)
% Number of variables : 1036 ( 78 sgn 446 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t236,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t273,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t236]) ).
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(t96,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t347,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t96]) ).
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(t344,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(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(t191,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(t285,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)],[t191]) ).
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(t106,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t106]) ).
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(t178,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(t271,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)],[t178]) ).
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(t159,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(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t159]) ).
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(t183,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(t308,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)],[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(t160,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(t357,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t160]) ).
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(t103,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t362,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t103]) ).
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(t305,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]) ).
fof(f17,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD18) ).
fof(f17_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t182,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t310,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(orient,[status(thm)],[t182]) ).
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(hi67,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(coll(X0,X1,X2),true,midp(X0,X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
fof(f94,conjecture,
! [O,X,L,A,Y,B,P,Q,Q1,P1] :
( ( coll(P1,L,B)
& coll(P1,O,X)
& coll(Q1,O,Y)
& coll(Q1,L,A)
& cong(L,B,L,Q)
& coll(L,B,Q)
& cong(L,A,L,P)
& coll(L,A,P)
& coll(B,O,Y)
& perp(B,L,O,Y)
& coll(A,O,X)
& perp(A,L,O,X) )
=> cyclic(O,P,Q,P1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL8110988) ).
fof(f94_neg,negated_conjecture,
~ ! [O,X,L,A,Y,B,P,Q,Q1,P1] :
( ( coll(P1,L,B)
& coll(P1,O,X)
& coll(Q1,O,Y)
& coll(Q1,L,A)
& cong(L,B,L,Q)
& coll(L,B,Q)
& cong(L,A,L,P)
& coll(L,A,P)
& coll(B,O,Y)
& perp(B,L,O,Y)
& coll(A,O,X)
& perp(A,L,O,X) )
=> cyclic(O,P,Q,P1) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [O,X,L,A,Y,B,P,Q,Q1,P1] :
( ~ cyclic(O,P,Q,P1)
& coll(P1,L,B)
& coll(P1,O,X)
& coll(Q1,O,Y)
& coll(Q1,L,A)
& cong(L,B,L,Q)
& coll(L,B,Q)
& cong(L,A,L,P)
& coll(L,A,P)
& coll(B,O,Y)
& perp(B,L,O,Y)
& coll(A,O,X)
& perp(A,L,O,X) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk20,sk26,sk27,sk29)
& coll(sk29,sk22,sk25)
& coll(sk29,sk20,sk21)
& coll(sk28,sk20,sk24)
& coll(sk28,sk22,sk23)
& cong(sk22,sk25,sk22,sk27)
& coll(sk22,sk25,sk27)
& cong(sk22,sk23,sk22,sk26)
& coll(sk22,sk23,sk26)
& coll(sk25,sk20,sk24)
& perp(sk25,sk22,sk20,sk24)
& coll(sk23,sk20,sk21)
& perp(sk23,sk22,sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29])],[f94_nnf]) ).
cnf(c118,plain,
cong(sk22,sk23,sk22,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
cong(sk22,sk23,sk22,sk26) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(c117,plain,
coll(sk22,sk23,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk22,sk23,sk26) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h13,plain,
midp(sk22,sk23,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi67,hi118,hi117]) ).
cnf(c120,plain,
cong(sk22,sk25,sk22,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
cong(sk22,sk25,sk22,sk27) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(c119,plain,
coll(sk22,sk25,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
coll(sk22,sk25,sk27) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h22,plain,
midp(sk22,sk25,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi67,hi120,hi119]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h116,plain,
para(sk25,sk23,sk27,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi63,h22,h13]) ).
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(h702,plain,
eqangle(sk25,sk23,V0,V1,sk27,sk26,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h116]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(c113,plain,
perp(sk23,sk22,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
perp(sk23,sk22,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk20,sk21,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi113]) ).
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(h41,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h0,hi113]) ).
cnf(h168,plain,
eqangle(sk20,sk21,V0,V1,sk20,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h41]) ).
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(h932,plain,
eqangle(sk20,sk21,sk20,sk21,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h168]) ).
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(t40,plain,
eqangle(sk20,sk21,sk20,sk21,sk27,sk26,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi21,h932,h702]) ).
cnf(t2099,plain,
eqangle(sk20,sk21,sk20,sk21,sk27,sk26,sk25,sk23) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t2102,plain,
true = ifeq(true,true,eqangle(sk21,sk20,sk20,sk21,sk27,sk26,sk25,sk23),true),
inference(cp,[status(thm)],[t310,t2099]) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t28]) ).
cnf(t26008,plain,
true = eqangle(sk21,sk20,sk20,sk21,sk27,sk26,sk25,sk23),
inference(step,[status(thm)],[t2102,t256]) ).
cnf(t6825,plain,
eqangle(sk21,sk20,sk20,sk21,sk27,sk26,sk25,sk23) = true,
inference(orient,[status(thm)],[t26008]) ).
cnf(t6832,plain,
true = ifeq(true,true,ifeq(para(sk27,sk26,sk25,sk23),true,para(sk21,sk20,sk20,sk21),true),true),
inference(cp,[status(thm)],[t305,t6825]) ).
cnf(t26009,plain,
true = ifeq(para(sk27,sk26,sk25,sk23),true,para(sk21,sk20,sk20,sk21),true),
inference(step,[status(thm)],[t6832,t256]) ).
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(t104,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t359,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t104]) ).
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(h933,plain,
eqangle(V0,V1,sk20,sk21,V0,V1,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi18,h168]) ).
cnf(t42,plain,
eqangle(sk25,sk23,sk20,sk21,sk27,sk26,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi21,h702,h933]) ).
cnf(t2083,plain,
eqangle(sk25,sk23,sk20,sk21,sk27,sk26,sk20,sk21) = true,
inference(orient,[status(thm)],[t42]) ).
cnf(t2085,plain,
true = ifeq(true,true,para(sk25,sk23,sk27,sk26),true),
inference(cp,[status(thm)],[t314,t2083]) ).
cnf(t25928,plain,
true = para(sk25,sk23,sk27,sk26),
inference(step,[status(thm)],[t2085,t256]) ).
cnf(t5228,plain,
para(sk25,sk23,sk27,sk26) = true,
inference(orient,[status(thm)],[t25928]) ).
cnf(t5231,plain,
true = ifeq(true,true,para(sk27,sk26,sk25,sk23),true),
inference(cp,[status(thm)],[t359,t5228]) ).
cnf(t25948,plain,
true = para(sk27,sk26,sk25,sk23),
inference(step,[status(thm)],[t5231,t256]) ).
cnf(t5627,plain,
para(sk27,sk26,sk25,sk23) = true,
inference(orient,[status(thm)],[t25948]) ).
cnf(t26010,plain,
true = ifeq(true,true,para(sk21,sk20,sk20,sk21),true),
inference(step,[status(thm)],[t26009,t5627]) ).
cnf(t26011,plain,
true = para(sk21,sk20,sk20,sk21),
inference(step,[status(thm)],[t26010,t256]) ).
cnf(t6837,plain,
para(sk21,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t26011]) ).
cnf(t6838,plain,
true = ifeq(true,true,para(sk21,sk20,sk21,sk20),true),
inference(cp,[status(thm)],[t362,t6837]) ).
cnf(t26012,plain,
true = para(sk21,sk20,sk21,sk20),
inference(step,[status(thm)],[t6838,t256]) ).
cnf(t6863,plain,
para(sk21,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t26012]) ).
cnf(t6865,plain,
true = ifeq(true,true,eqangle(sk21,sk20,X1,X2,sk21,sk20,X1,X2),true),
inference(cp,[status(thm)],[t357,t6863]) ).
cnf(t26235,plain,
true = eqangle(sk21,sk20,X1,X2,sk21,sk20,X1,X2),
inference(step,[status(thm)],[t6865,t256]) ).
cnf(t10307,plain,
eqangle(sk21,sk20,X1,X2,sk21,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t26235]) ).
cnf(t10313,plain,
true = ifeq(true,true,eqangle(X1,X2,sk21,sk20,X1,X2,sk21,sk20),true),
inference(cp,[status(thm)],[t308,t10307]) ).
cnf(t26485,plain,
true = eqangle(X1,X2,sk21,sk20,X1,X2,sk21,sk20),
inference(step,[status(thm)],[t10313,t256]) ).
cnf(t12908,plain,
eqangle(X1,X2,sk21,sk20,X1,X2,sk21,sk20) = true,
inference(orient,[status(thm)],[t26485]) ).
cnf(t12910,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t12908]) ).
cnf(t26486,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t12910,t256]) ).
cnf(t12932,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t26486]) ).
cnf(t12949,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)],[t344,t12932]) ).
cnf(t27815,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)],[t12949,t256]) ).
cnf(t27816,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t27815,t12932]) ).
cnf(t27817,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t27816,t256]) ).
cnf(t24652,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t27817]) ).
cnf(t169,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(t272,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)],[t169]) ).
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(t98,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t268,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t98]) ).
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(t99,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t266,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t99]) ).
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(t323,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(t158,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(t327,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t158]) ).
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(c123,plain,
coll(sk29,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi123,negated_conjecture,
coll(sk29,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c123]) ).
cnf(h36,plain,
coll(sk29,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi123]) ).
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(h157,plain,
coll(sk20,sk20,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi2,h36,h36]) ).
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(h927,plain,
cyclic(sk21,sk29,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h168,h157]) ).
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(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t22,plain,
cyclic(sk21,sk20,sk29,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h927]) ).
cnf(t2264,plain,
cyclic(sk21,sk20,sk29,sk20) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t2271,plain,
true = ifeq(true,true,eqangle(sk29,sk21,sk29,sk20,sk20,sk21,sk20,sk20),true),
inference(cp,[status(thm)],[t327,t2264]) ).
cnf(t26027,plain,
true = eqangle(sk29,sk21,sk29,sk20,sk20,sk21,sk20,sk20),
inference(step,[status(thm)],[t2271,t256]) ).
cnf(t7174,plain,
eqangle(sk29,sk21,sk29,sk20,sk20,sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t26027]) ).
cnf(t7190,plain,
true = ifeq(cyclic(sk21,sk20,sk29,sk21),true,ifeq(cyclic(sk21,sk20,sk29,sk20),true,ifeq(cyclic(sk21,sk20,sk29,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),true),true),
inference(cp,[status(thm)],[t323,t7174]) ).
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(t100,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t332,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t100]) ).
cnf(t101,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t330,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t101]) ).
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(h35,plain,
coll(sk20,sk29,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi123]) ).
cnf(t23,plain,
cyclic(sk21,sk21,sk20,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi42,h932,h35]) ).
cnf(t2284,plain,
cyclic(sk21,sk21,sk20,sk29) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t2287,plain,
true = ifeq(true,true,cyclic(sk21,sk20,sk21,sk29),true),
inference(cp,[status(thm)],[t330,t2284]) ).
cnf(t25932,plain,
true = cyclic(sk21,sk20,sk21,sk29),
inference(step,[status(thm)],[t2287,t256]) ).
cnf(t5311,plain,
cyclic(sk21,sk20,sk21,sk29) = true,
inference(orient,[status(thm)],[t25932]) ).
cnf(t5312,plain,
true = ifeq(true,true,cyclic(sk21,sk20,sk29,sk21),true),
inference(cp,[status(thm)],[t332,t5311]) ).
cnf(t25952,plain,
true = cyclic(sk21,sk20,sk29,sk21),
inference(step,[status(thm)],[t5312,t256]) ).
cnf(t5708,plain,
cyclic(sk21,sk20,sk29,sk21) = true,
inference(orient,[status(thm)],[t25952]) ).
cnf(t26028,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk20,sk29,sk20),true,ifeq(cyclic(sk21,sk20,sk29,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),true),true),
inference(step,[status(thm)],[t7190,t5708]) ).
cnf(t26029,plain,
true = ifeq(cyclic(sk21,sk20,sk29,sk20),true,ifeq(cyclic(sk21,sk20,sk29,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),true),
inference(step,[status(thm)],[t26028,t256]) ).
cnf(t26030,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk20,sk29,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),true),
inference(step,[status(thm)],[t26029,t2264]) ).
cnf(t26031,plain,
true = ifeq(cyclic(sk21,sk20,sk29,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),
inference(step,[status(thm)],[t26030,t256]) ).
cnf(t26032,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),
inference(step,[status(thm)],[t26031,t2264]) ).
cnf(t26033,plain,
true = ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),
inference(step,[status(thm)],[t26032,t256]) ).
cnf(t26034,plain,
true = cong(sk21,sk20,sk21,sk20),
inference(step,[status(thm)],[t26033,t256]) ).
cnf(t7191,plain,
cong(sk21,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t26034]) ).
cnf(t7194,plain,
true = ifeq(true,true,cong(sk21,sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t268,t7191]) ).
cnf(t26038,plain,
true = cong(sk21,sk20,sk20,sk21),
inference(step,[status(thm)],[t7194,t256]) ).
cnf(t7259,plain,
cong(sk21,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t26038]) ).
cnf(t7261,plain,
true = ifeq(true,true,cong(sk20,sk21,sk21,sk20),true),
inference(cp,[status(thm)],[t266,t7259]) ).
cnf(t26039,plain,
true = cong(sk20,sk21,sk21,sk20),
inference(step,[status(thm)],[t7261,t256]) ).
cnf(t7269,plain,
cong(sk20,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t26039]) ).
cnf(t7271,plain,
true = ifeq(true,true,cong(sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t268,t7269]) ).
cnf(t26040,plain,
true = cong(sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t7271,t256]) ).
cnf(t7278,plain,
cong(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t26040]) ).
cnf(t7288,plain,
true = ifeq(true,true,ifeq(coll(sk20,sk21,sk21),true,midp(sk20,sk21,sk21),true),true),
inference(cp,[status(thm)],[t272,t7278]) ).
cnf(t26041,plain,
true = ifeq(coll(sk20,sk21,sk21),true,midp(sk20,sk21,sk21),true),
inference(step,[status(thm)],[t7288,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(t97,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t365,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t97]) ).
cnf(t6839,plain,
true = ifeq(true,true,para(sk20,sk21,sk21,sk20),true),
inference(cp,[status(thm)],[t359,t6837]) ).
cnf(t26016,plain,
true = para(sk20,sk21,sk21,sk20),
inference(step,[status(thm)],[t6839,t256]) ).
cnf(t6980,plain,
para(sk20,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t26016]) ).
cnf(t6981,plain,
true = ifeq(true,true,para(sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t362,t6980]) ).
cnf(t26017,plain,
true = para(sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t6981,t256]) ).
cnf(t7004,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t26017]) ).
cnf(t7005,plain,
true = ifeq(true,true,coll(sk20,sk21,sk21),true),
inference(cp,[status(thm)],[t365,t7004]) ).
cnf(t26018,plain,
true = coll(sk20,sk21,sk21),
inference(step,[status(thm)],[t7005,t256]) ).
cnf(t7029,plain,
coll(sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t26018]) ).
cnf(t26042,plain,
true = ifeq(true,true,midp(sk20,sk21,sk21),true),
inference(step,[status(thm)],[t26041,t7029]) ).
cnf(t26043,plain,
true = midp(sk20,sk21,sk21),
inference(step,[status(thm)],[t26042,t256]) ).
cnf(t7317,plain,
midp(sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t26043]) ).
cnf(t24653,plain,
true = ifeq(true,true,midp(sk20,X1,X1),true),
inference(cp,[status(thm)],[t24652,t7317]) ).
cnf(t27818,plain,
true = midp(sk20,X1,X1),
inference(step,[status(thm)],[t24653,t256]) ).
cnf(t24656,plain,
midp(sk20,X1,X1) = true,
inference(orient,[status(thm)],[t27818]) ).
cnf(t24657,plain,
true = ifeq(true,true,cong(sk20,X1,sk20,X1),true),
inference(cp,[status(thm)],[t347,t24656]) ).
cnf(t27820,plain,
true = cong(sk20,X1,sk20,X1),
inference(step,[status(thm)],[t24657,t256]) ).
cnf(t24696,plain,
cong(sk20,X1,sk20,X1) = true,
inference(orient,[status(thm)],[t27820]) ).
cnf(t24707,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t24696]) ).
cnf(t27823,plain,
true = ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t24707,t256]) ).
cnf(t27824,plain,
true = ifeq(true,true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t27823,t24696]) ).
cnf(t27825,plain,
true = perp(sk20,sk20,X2,X1),
inference(step,[status(thm)],[t27824,t256]) ).
cnf(t24796,plain,
perp(sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t27825]) ).
cnf(t24797,plain,
true = ifeq(true,true,perp(X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t292,t24796]) ).
cnf(t27831,plain,
true = perp(X1,X2,sk20,sk20),
inference(step,[status(thm)],[t24797,t256]) ).
cnf(t24904,plain,
perp(X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t27831]) ).
cnf(t24911,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t24904]) ).
cnf(t27835,plain,
true = ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t24911,t256]) ).
cnf(t27836,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t27835,t24796]) ).
cnf(t27837,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t27836,t256]) ).
cnf(t25007,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t27837]) ).
cnf(t27849,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t344,t25007]) ).
cnf(t27850,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t27849,t256]) ).
cnf(t27851,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t27850,t25007]) ).
cnf(t27852,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t27851,t256]) ).
cnf(t25014,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t27852]) ).
cnf(t25641,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t25014]) ).
cnf(t7203,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk20,sk20),true,midp(sk21,sk20,sk20),true),true),
inference(cp,[status(thm)],[t272,t7191]) ).
cnf(t26035,plain,
true = ifeq(coll(sk21,sk20,sk20),true,midp(sk21,sk20,sk20),true),
inference(step,[status(thm)],[t7203,t256]) ).
cnf(t6864,plain,
true = ifeq(true,true,coll(sk21,sk20,sk20),true),
inference(cp,[status(thm)],[t365,t6863]) ).
cnf(t26013,plain,
true = coll(sk21,sk20,sk20),
inference(step,[status(thm)],[t6864,t256]) ).
cnf(t6888,plain,
coll(sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t26013]) ).
cnf(t26036,plain,
true = ifeq(true,true,midp(sk21,sk20,sk20),true),
inference(step,[status(thm)],[t26035,t6888]) ).
cnf(t26037,plain,
true = midp(sk21,sk20,sk20),
inference(step,[status(thm)],[t26036,t256]) ).
cnf(t7232,plain,
midp(sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t26037]) ).
cnf(t24655,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t24652,t7232]) ).
cnf(t27819,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t24655,t256]) ).
cnf(t24676,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t27819]) ).
cnf(t25642,plain,
true = ifeq(true,true,midp(sk21,X1,X2),true),
inference(cp,[status(thm)],[t25641,t24676]) ).
cnf(t27933,plain,
true = midp(sk21,X1,X2),
inference(step,[status(thm)],[t25642,t256]) ).
cnf(t25666,plain,
midp(sk21,X1,X2) = true,
inference(orient,[status(thm)],[t27933]) ).
cnf(t25667,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X2),true),
inference(cp,[status(thm)],[t347,t25666]) ).
cnf(t27937,plain,
true = cong(sk21,X1,sk21,X2),
inference(step,[status(thm)],[t25667,t256]) ).
cnf(t25706,plain,
cong(sk21,X1,sk21,X2) = true,
inference(orient,[status(thm)],[t27937]) ).
cnf(t25724,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X2),true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),true),
inference(cp,[status(thm)],[t273,t25706]) ).
cnf(t27961,plain,
true = ifeq(cong(sk21,X1,sk21,X2),true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),
inference(step,[status(thm)],[t25724,t256]) ).
cnf(t27962,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),
inference(step,[status(thm)],[t27961,t25706]) ).
cnf(t27963,plain,
true = ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),
inference(step,[status(thm)],[t27962,t256]) ).
cnf(t27964,plain,
true = ifeq(true,true,cyclic(X1,X4,X2,X3),true),
inference(step,[status(thm)],[t27963,t25706]) ).
cnf(t27965,plain,
true = cyclic(X1,X4,X2,X3),
inference(step,[status(thm)],[t27964,t256]) ).
cnf(t25863,plain,
cyclic(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t27965]) ).
cnf(c125,plain,
~ cyclic(sk20,sk26,sk27,sk29),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk20,sk26,sk27,sk29) != true,
inference(equality_encoding,[status(esa)],[c125]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t25863]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO624+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/10.32 % Computer : n012.cluster.edu
% 0.03/10.32 % Model : x86_64 x86_64
% 0.03/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.32 % Memory : 8046.5625MB
% 0.03/10.32 % OS : Linux 6.8.0-71-generic
% 0.03/10.32 % CPULimit : 300
% 0.03/10.32 % WCLimit : 300
% 0.03/10.32 % DateTime : Wed Sep 23 12:35:12 UTC 2026
% 0.03/10.32 % CPUTime :
% 0.03/10.32 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 94.49/22.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 94.49/22.62 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------