%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG055+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 02:38:27 PM UTC 2026
% Result : Theorem 3.33s 22.66s
% Output : CNFRefutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 109 ( 35 unt; 0 def)
% Number of atoms : 268 ( 159 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 305 ( 146 ~; 140 |; 17 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 99 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
fof(f44,axiom,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
fof(f45,axiom,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
fof(f48,axiom,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
fof(f51,axiom,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).
fof(f53,axiom,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
fof(f57,conjecture,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f58,negated_conjecture,
sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f64,plain,
sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(flattening,[],[f58]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f73]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
inference(flattening,[],[f77]) ).
fof(f133,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f135,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f191,plain,
aScalar0(xA),
inference(cnf_transformation,[],[f44]) ).
fof(f193,plain,
aScalar0(xB),
inference(cnf_transformation,[],[f45]) ).
fof(f198,plain,
xE = sdtasasdt0(xp,xq),
inference(cnf_transformation,[],[f48]) ).
fof(f199,plain,
aScalar0(xE),
inference(cnf_transformation,[],[f48]) ).
fof(f204,plain,
xH = sdtasdt0(xA,xB),
inference(cnf_transformation,[],[f51]) ).
fof(f205,plain,
aScalar0(xH),
inference(cnf_transformation,[],[f51]) ).
fof(f208,plain,
xP = sdtasdt0(xE,xH),
inference(cnf_transformation,[],[f53]) ).
fof(f215,plain,
sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(cnf_transformation,[],[f64]) ).
tcf(c_56,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f133]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_113,plain,
aScalar0(xA),
inference(cnf_transformation,[],[f191]) ).
tcf(c_115,plain,
aScalar0(xB),
inference(cnf_transformation,[],[f193]) ).
tcf(c_121,plain,
aScalar0(xE),
inference(cnf_transformation,[],[f199]) ).
tcf(c_122,plain,
sdtasasdt0(xp,xq) = xE,
inference(cnf_transformation,[],[f198]) ).
tcf(c_127,plain,
aScalar0(xH),
inference(cnf_transformation,[],[f205]) ).
tcf(c_128,plain,
sdtasdt0(xA,xB) = xH,
inference(cnf_transformation,[],[f204]) ).
tcf(c_132,plain,
sdtasdt0(xE,xH) = xP,
inference(cnf_transformation,[],[f208]) ).
tcf(c_138,negated_conjecture,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(xP,xP),
inference(cnf_transformation,[],[f215]) ).
tcf(c_1132,negated_conjecture,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(xP,xP),
inference(subtyping,[status(esa)],[c_138]) ).
tcf(c_1138,plain,
sdtasdt0(xE,xH) = xP,
inference(subtyping,[status(esa)],[c_132]) ).
tcf(c_1142,plain,
sdtasdt0(xA,xB) = xH,
inference(subtyping,[status(esa)],[c_128]) ).
tcf(c_1143,plain,
aScalar0(xH),
inference(subtyping,[status(esa)],[c_127]) ).
tcf(c_1148,plain,
sdtasasdt0(xp,xq) = xE,
inference(subtyping,[status(esa)],[c_122]) ).
tcf(c_1149,plain,
aScalar0(xE),
inference(subtyping,[status(esa)],[c_121]) ).
tcf(c_1198,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) )
| ~ aScalar0(X2_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_71]) ).
tcf(c_1199,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),X2_iProver_sdtasdt0_2) = sdtasdt0(X0_iProver_sdtasdt0_2,sdtasdt0(X1_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2)) )
| ~ aScalar0(X2_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_70]) ).
tcf(c_1200,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtpldt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtpldt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) )
| ~ aScalar0(X2_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_1210,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( aScalar0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2))
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_1219,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ~ iPr_def_10
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_1200]) ).
tcf(c_1222,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ~ iPr_def_12
| ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) )
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_1198]) ).
tcf(c_1223,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1198]) ).
tcf(c_1227,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] : X0_iProver_sdtasdt0_2 = X0_iProver_sdtasdt0_2,
theory(equality) ).
tcf(c_1230,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( X2_iProver_sdtasdt0_2 = X0_iProver_sdtasdt0_2 )
| ( X2_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 ) ),
theory(equality) ).
tcf(c_1235,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(X0_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2) )
| ( X2_iProver_sdtasdt0_2 != X3_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 ) ),
theory(equality) ).
tcf(c_1284,plain,
( ~ iPr_def_10
| ~ aScalar0(sz0z00) ),
inference(instantiation,[status(thm)],[c_1219]) ).
tcf(c_1294,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ~ aScalar0(X0_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_1222,c_56,c_1284,c_1222,c_1223]) ).
tcf(c_1295,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) )
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(renaming,[status(thm)],[c_1294]) ).
tcf(c_2364,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xH,X0_iProver_sdtasdt0_2),X1_iProver_sdtasdt0_2) = sdtasdt0(xH,sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2)) )
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(superposition,[status(thm)],[c_1143,c_1199]) ).
tcf(c_2393,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = X1_iProver_sdtasdt0_2 )
| ( X1_iProver_sdtasdt0_2 != X0_iProver_sdtasdt0_2 )
| ( sdtasdt0(xP,xP) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1230]) ).
tcf(c_2395,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) )
| ( xP != X1_iProver_sdtasdt0_2 )
| ( xP != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1235]) ).
tcf(c_2407,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( xP = X0_iProver_sdtasdt0_2 )
| ( xP != X1_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1230]) ).
tcf(c_2425,plain,
xP = xP,
inference(instantiation,[status(thm)],[c_1227]) ).
tcf(c_2462,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( xP = X0_iProver_sdtasdt0_2 )
| ( xP != xP )
| ( X0_iProver_sdtasdt0_2 != xP ) ),
inference(instantiation,[status(thm)],[c_2407]) ).
tcf(c_2478,plain,
( ( xP = sdtasdt0(xE,xH) )
| ( xP != xP )
| ( sdtasdt0(xE,xH) != xP ) ),
inference(instantiation,[status(thm)],[c_2462]) ).
tcf(c_2514,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( xP = X0_iProver_sdtasdt0_2 )
| ( xP != sdtasdt0(xE,xH) )
| ( X0_iProver_sdtasdt0_2 != sdtasdt0(xE,xH) ) ),
inference(instantiation,[status(thm)],[c_2407]) ).
tcf(c_2581,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( X1_iProver_sdtasdt0_2 = X0_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 ) ),
inference(resolution,[status(thm)],[c_1230,c_1227]) ).
tcf(c_2615,plain,
( ( xP = sdtasdt0(xH,xE) )
| ( xP != sdtasdt0(xE,xH) )
| ( sdtasdt0(xH,xE) != sdtasdt0(xE,xH) ) ),
inference(instantiation,[status(thm)],[c_2514]) ).
tcf(c_2616,plain,
( ( sdtasdt0(xH,xE) = sdtasdt0(xE,xH) )
| ~ aScalar0(xH)
| ~ aScalar0(xE) ),
inference(instantiation,[status(thm)],[c_1295]) ).
tcf(c_2620,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( xP = sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) )
| ( xP != sdtasdt0(xE,xH) )
| ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) != sdtasdt0(xE,xH) ) ),
inference(instantiation,[status(thm)],[c_2514]) ).
tcf(c_2621,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(xE,xH) )
| ( X1_iProver_sdtasdt0_2 != xH )
| ( X0_iProver_sdtasdt0_2 != xE ) ),
inference(instantiation,[status(thm)],[c_1235]) ).
tcf(c_2646,plain,
xE = sdtasasdt0(xp,xq),
inference(resolution,[status(thm)],[c_2581,c_1148]) ).
tcf(c_2832,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(X0_iProver_sdtasdt0_2,sdtasdt0(xA,xB)) = sdtasdt0(xE,xH) )
| ( X0_iProver_sdtasdt0_2 != xE )
| ( sdtasdt0(xA,xB) != xH ) ),
inference(instantiation,[status(thm)],[c_2621]) ).
tcf(c_2885,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( xE = X0_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != sdtasasdt0(xp,xq) ) ),
inference(resolution,[status(thm)],[c_2646,c_1230]) ).
tcf(c_3011,plain,
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) )
| ~ aScalar0(xH)
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(instantiation,[status(thm)],[c_1199]) ).
tcf(c_3013,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(instantiation,[status(thm)],[c_1227]) ).
tcf(c_3014,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = X1_iProver_sdtasdt0_2 )
| ( X1_iProver_sdtasdt0_2 != X0_iProver_sdtasdt0_2 )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1230]) ).
tcf(c_3198,plain,
xE = xE,
inference(resolution,[status(thm)],[c_2885,c_2646]) ).
tcf(c_3271,plain,
( ( sdtasdt0(xE,sdtasdt0(xA,xB)) = sdtasdt0(xE,xH) )
| ( xE != xE )
| ( sdtasdt0(xA,xB) != xH ) ),
inference(instantiation,[status(thm)],[c_2832]) ).
tcf(c_3696,plain,
( aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(xE) ),
inference(instantiation,[status(thm)],[c_1210]) ).
tcf(c_3860,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = X0_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) ) ),
inference(instantiation,[status(thm)],[c_3014]) ).
tcf(c_4125,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xH,xE),X0_iProver_sdtasdt0_2) = sdtasdt0(xH,sdtasdt0(xE,X0_iProver_sdtasdt0_2)) )
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(superposition,[status(thm)],[c_1149,c_2364]) ).
tcf(c_4196,plain,
( ( xP = sdtasdt0(xE,sdtasdt0(xA,xB)) )
| ( xP != sdtasdt0(xE,xH) )
| ( sdtasdt0(xE,sdtasdt0(xA,xB)) != sdtasdt0(xE,xH) ) ),
inference(instantiation,[status(thm)],[c_2620]) ).
tcf(c_4291,plain,
sdtasdt0(sdtasdt0(xH,xE),xE) = sdtasdt0(xH,sdtasdt0(xE,xE)),
inference(superposition,[status(thm)],[c_1149,c_4125]) ).
tcf(c_4390,plain,
( aScalar0(sdtasdt0(xH,xE))
| ~ aScalar0(xH)
| ~ aScalar0(xE) ),
inference(instantiation,[status(thm)],[c_1210]) ).
tcf(c_5301,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = sdtasdt0(X0_iProver_sdtasdt0_2,sdtasdt0(xE,sdtasdt0(xA,xB))) )
| ( xP != X0_iProver_sdtasdt0_2 )
| ( xP != sdtasdt0(xE,sdtasdt0(xA,xB)) ) ),
inference(instantiation,[status(thm)],[c_2395]) ).
tcf(c_5344,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) )
| ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) ) ),
inference(instantiation,[status(thm)],[c_3860]) ).
tcf(c_6072,plain,
( ( sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xE),sdtasdt0(xE,sdtasdt0(xA,xB))) )
| ( xP != sdtasdt0(xH,xE) )
| ( xP != sdtasdt0(xE,sdtasdt0(xA,xB)) ) ),
inference(instantiation,[status(thm)],[c_5301]) ).
tcf(c_11473,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = X0_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != sdtasdt0(sdtasdt0(xH,xE),sdtasdt0(xE,sdtasdt0(xA,xB))) )
| ( sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xE),sdtasdt0(xE,sdtasdt0(xA,xB))) ) ),
inference(instantiation,[status(thm)],[c_2393]) ).
tcf(c_11985,plain,
( aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(xB)
| ~ aScalar0(xA) ),
inference(instantiation,[status(thm)],[c_1210]) ).
tcf(c_17028,plain,
( ( sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(sdtasdt0(xH,xE),xE),sdtasdt0(xA,xB)) )
| ( sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xE),sdtasdt0(xE,sdtasdt0(xA,xB))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xH,xE),xE),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xH,xE),sdtasdt0(xE,sdtasdt0(xA,xB))) ) ),
inference(instantiation,[status(thm)],[c_11473]) ).
tcf(c_17029,plain,
( ( sdtasdt0(sdtasdt0(sdtasdt0(xH,xE),xE),sdtasdt0(xA,xB)) = sdtasdt0(sdtasdt0(xH,xE),sdtasdt0(xE,sdtasdt0(xA,xB))) )
| ~ aScalar0(xE)
| ~ aScalar0(sdtasdt0(xH,xE))
| ~ aScalar0(sdtasdt0(xA,xB)) ),
inference(instantiation,[status(thm)],[c_1199]) ).
tcf(c_17668,plain,
( aScalar0(sdtasdt0(sdtasdt0(xH,xE),xE))
| ~ aScalar0(xE)
| ~ aScalar0(sdtasdt0(xH,xE)) ),
inference(instantiation,[status(thm)],[c_1210]) ).
tcf(c_25067,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = X0_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != sdtasdt0(sdtasdt0(sdtasdt0(xH,xE),xE),sdtasdt0(xA,xB)) )
| ( sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(sdtasdt0(xH,xE),xE),sdtasdt0(xA,xB)) ) ),
inference(instantiation,[status(thm)],[c_2393]) ).
tcf(c_30839,plain,
( ( sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtasdt0(xH,xE),xE)) )
| ( sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(sdtasdt0(xH,xE),xE),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtasdt0(xH,xE),xE)) != sdtasdt0(sdtasdt0(sdtasdt0(xH,xE),xE),sdtasdt0(xA,xB)) ) ),
inference(instantiation,[status(thm)],[c_25067]) ).
tcf(c_30840,plain,
( ( sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtasdt0(xH,xE),xE)) = sdtasdt0(sdtasdt0(sdtasdt0(xH,xE),xE),sdtasdt0(xA,xB)) )
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(sdtasdt0(xH,xE),xE)) ),
inference(instantiation,[status(thm)],[c_1295]) ).
tcf(c_40173,plain,
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(xP,xP) )
| ( sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) ) ),
inference(instantiation,[status(thm)],[c_5344]) ).
tcf(c_54037,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = X1_iProver_sdtasdt0_2 )
| ( X1_iProver_sdtasdt0_2 != X0_iProver_sdtasdt0_2 )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1230]) ).
tcf(c_54046,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(xP,xP) != X0_iProver_sdtasdt0_2 )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1230]) ).
tcf(c_54061,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = X0_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) ) ),
inference(instantiation,[status(thm)],[c_54037]) ).
tcf(c_54123,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) )
| ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) != sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) ) ),
inference(instantiation,[status(thm)],[c_54061]) ).
tcf(c_54124,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) )
| ( X1_iProver_sdtasdt0_2 != sdtasdt0(xH,sdtasdt0(xE,xE)) )
| ( X0_iProver_sdtasdt0_2 != xH ) ),
inference(instantiation,[status(thm)],[c_1235]) ).
tcf(c_54297,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtasdt0(xA,xB),X0_iProver_sdtasdt0_2) = sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) )
| ( X0_iProver_sdtasdt0_2 != sdtasdt0(xH,sdtasdt0(xE,xE)) )
| ( sdtasdt0(xA,xB) != xH ) ),
inference(instantiation,[status(thm)],[c_54124]) ).
tcf(c_54572,plain,
( ( sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtasdt0(xH,xE),xE)) = sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) )
| ( sdtasdt0(xA,xB) != xH )
| ( sdtasdt0(sdtasdt0(xH,xE),xE) != sdtasdt0(xH,sdtasdt0(xE,xE)) ) ),
inference(instantiation,[status(thm)],[c_54297]) ).
tcf(c_54950,plain,
( ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtasdt0(xH,xE),xE)) )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtasdt0(xH,xE),xE)) != sdtasdt0(xH,sdtasdt0(xH,sdtasdt0(xE,xE))) ) ),
inference(instantiation,[status(thm)],[c_54123]) ).
tcf(c_55383,plain,
( ( sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtasdt0(xH,xE),xE)) )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtasdt0(xH,xE),xE)) ) ),
inference(instantiation,[status(thm)],[c_54046]) ).
tcf(c_55387,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_55383,c_54950,c_54572,c_40173,c_30840,c_30839,c_17668,c_17029,c_17028,c_11985,c_6072,c_4390,c_4291,c_4196,c_3696,c_3271,c_3198,c_3013,c_3011,c_2616,c_2615,c_2478,c_2425,c_1142,c_1138,c_1132,c_113,c_115,c_121,c_127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG055+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 07:59:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 3.33/22.66 % SZS status Started for theBenchmark.p
% 3.33/22.66 % SZS status Theorem for theBenchmark.p
% 3.33/22.66
% 3.33/22.66 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.33/22.66
% 3.33/22.66 % ------ iProver source info
% 3.33/22.66
% 3.33/22.66 % git: date: 2026-07-19 20:42:38 +0200
% 3.33/22.66 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.33/22.66 % git: non_committed_changes: false
% 3.33/22.66
% 3.33/22.66 % ------ Parsing...
% 3.33/22.66 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.33/22.66
% 3.33/22.66 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.33/22.66
% 3.33/22.66 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.33/22.66
% 3.33/22.66 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 3.33/22.66 % ------ Proving...
% 3.33/22.66 % ------ Problem Properties
% 3.33/22.66
% 3.33/22.66 %
% 3.33/22.66 % clauses 92
% 3.33/22.66 % conjectures 1
% 3.33/22.66 % EPR 25
% 3.33/22.66 % Horn 80
% 3.33/22.66 % unary 39
% 3.33/22.66 % binary 19
% 3.33/22.66 % lits 226
% 3.33/22.66 % lits eq 72
% 3.33/22.66 % fd_pure 0
% 3.33/22.66 % fd_pseudo 0
% 3.33/22.66 % fd_cond 1
% 3.33/22.66 % fd_pseudo_cond 5
% 3.33/22.66 % AC symbols 0
% 3.33/22.66
% 3.33/22.66 % ------ Input Options Time Limit: Unbounded
% 3.33/22.66
% 3.33/22.66
% 3.33/22.66 % ------
% 3.33/22.66 % Current options:
% 3.33/22.66 % ------
% 3.33/22.66
% 3.33/22.66
% 3.33/22.66 %
% 3.33/22.66
% 3.33/22.66 % ------ Proving...
% 3.33/22.66 %
% 3.33/22.66
% 3.33/22.66 % SZS status Theorem for theBenchmark.p
% 3.33/22.66
% 3.33/22.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.33/22.66
% 3.33/22.66
%------------------------------------------------------------------------------