%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 02:38:09 PM UTC 2026
% Result : Unsatisfiable 2.88s 0.99s
% Output : CNFRefutation 2.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 62 unt; 1 def)
% Number of atoms : 194 ( 56 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 53 ( 29 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
fof(f18,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_inverse_c) ).
fof(f19,axiom,
product(a,b,aPb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f20,axiom,
product(a,c,aPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c) ).
fof(f21,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
fof(f22,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
tcf(c_71,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_72,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_76,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X6,X2,X5)
| ~ product(X6,X1,X4)
| ~ product(X6,X0,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_88,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(cnf_transformation,[],[f18]) ).
tcf(c_89,plain,
product(a,b,aPb),
inference(cnf_transformation,[],[f19]) ).
tcf(c_90,plain,
product(a,c,aPc),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(cnf_transformation,[],[f22]) ).
tcf(c_100,plain,
add(b,additive_inverse(c)) = bS_Ic,
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_101,plain,
multiply(a,b) = aPb,
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_102,plain,
multiply(a,c) = aPc,
inference(well_definedness,[status(thm)],[c_90]) ).
tcf(c_103,plain,
add(aPb,additive_inverse(aPc)) = aPb_S_IaPc,
inference(well_definedness,[status(thm)],[c_91]) ).
tcf(c_104,plain,
multiply(a,bS_Ic) != aPb_S_IaPc,
inference(well_definedness,[status(thm)],[c_92]) ).
tcf(c_105,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_106,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_110,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_115]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_113]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_123]) ).
tcf(c_302,definition,
iPr_def_10 = multiply(a,bS_Ic),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_303,plain,
iPr_def_10 != aPb_S_IaPc,
inference(demodulation,[status(thm)],[c_104,c_302]) ).
tcf(c_381,plain,
! [X0: $i] : add(b,add(additive_inverse(c),X0)) = add(bS_Ic,X0),
inference(superposition,[status(thm)],[c_100,c_256]) ).
tcf(c_382,plain,
! [X0: $i] : add(aPb,add(additive_inverse(aPc),X0)) = add(aPb_S_IaPc,X0),
inference(superposition,[status(thm)],[c_103,c_256]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_110,c_256]) ).
tcf(c_397,plain,
add(bS_Ic,additive_inverse(additive_inverse(c))) = add(b,additive_identity),
inference(superposition,[status(thm)],[c_110,c_381]) ).
tcf(c_402,plain,
add(bS_Ic,additive_inverse(additive_inverse(c))) = add(additive_identity,b),
inference(theory_normalisation,[status(thm)],[c_397,c_256,c_250]) ).
tcf(c_404,plain,
add(bS_Ic,additive_inverse(additive_inverse(c))) = b,
inference(demodulation,[status(thm)],[c_402,c_105]) ).
tcf(c_409,plain,
add(aPb_S_IaPc,additive_inverse(additive_inverse(aPc))) = add(aPb,additive_identity),
inference(superposition,[status(thm)],[c_110,c_382]) ).
tcf(c_414,plain,
add(aPb_S_IaPc,additive_inverse(additive_inverse(aPc))) = add(additive_identity,aPb),
inference(theory_normalisation,[status(thm)],[c_409,c_256,c_250]) ).
tcf(c_416,plain,
add(aPb_S_IaPc,additive_inverse(additive_inverse(aPc))) = aPb,
inference(demodulation,[status(thm)],[c_414,c_105]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_385,c_105]) ).
tcf(c_424,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_110,c_419]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_250,c_419]) ).
tcf(c_436,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_424,c_106]) ).
tcf(c_438,plain,
add(bS_Ic,c) = b,
inference(demodulation,[status(thm)],[c_404,c_436]) ).
tcf(c_439,plain,
add(aPb_S_IaPc,aPc) = aPb,
inference(demodulation,[status(thm)],[c_416,c_436]) ).
tcf(c_440,plain,
add(aPc,aPb_S_IaPc) = aPb,
inference(theory_normalisation,[status(thm)],[c_439,c_256,c_250]) ).
tcf(c_441,plain,
add(c,bS_Ic) = b,
inference(theory_normalisation,[status(thm)],[c_438,c_256,c_250]) ).
tcf(c_447,plain,
! [X0: $i] : add(aPc,add(aPb_S_IaPc,X0)) = add(aPb,X0),
inference(superposition,[status(thm)],[c_440,c_256]) ).
tcf(c_492,plain,
! [X0: $i] : add(multiply(X0,c),multiply(X0,bS_Ic)) = multiply(X0,b),
inference(superposition,[status(thm)],[c_441,c_260]) ).
tcf(c_560,plain,
! [X0: $i] : add(aPb,add(additive_inverse(aPb_S_IaPc),X0)) = add(aPc,X0),
inference(superposition,[status(thm)],[c_419,c_447]) ).
tcf(c_730,plain,
add(aPc,additive_inverse(aPb)) = additive_inverse(aPb_S_IaPc),
inference(superposition,[status(thm)],[c_560,c_425]) ).
tcf(c_1794,plain,
add(multiply(a,c),iPr_def_10) = multiply(a,b),
inference(superposition,[status(thm)],[c_302,c_492]) ).
tcf(c_1805,plain,
add(iPr_def_10,multiply(a,c)) = multiply(a,b),
inference(theory_normalisation,[status(thm)],[c_1794,c_256,c_250]) ).
tcf(c_1806,plain,
add(iPr_def_10,aPc) = aPb,
inference(light_normalisation,[status(thm)],[c_1805,c_101,c_102]) ).
tcf(c_1815,plain,
! [X0: $i] : add(iPr_def_10,add(aPc,X0)) = add(aPb,X0),
inference(superposition,[status(thm)],[c_1806,c_256]) ).
tcf(c_1861,plain,
add(aPb,additive_inverse(iPr_def_10)) = aPc,
inference(superposition,[status(thm)],[c_1815,c_425]) ).
tcf(c_1874,plain,
! [X0: $i] : add(aPb,add(additive_inverse(iPr_def_10),X0)) = add(aPc,X0),
inference(superposition,[status(thm)],[c_1861,c_256]) ).
tcf(c_2124,plain,
add(aPc,additive_inverse(aPb)) = additive_inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_1874,c_425]) ).
tcf(c_2137,plain,
additive_inverse(aPb_S_IaPc) = additive_inverse(iPr_def_10),
inference(demodulation,[status(thm)],[c_730,c_2124]) ).
tcf(c_2139,plain,
additive_inverse(additive_inverse(iPr_def_10)) = aPb_S_IaPc,
inference(superposition,[status(thm)],[c_2137,c_436]) ).
tcf(c_2142,plain,
aPb_S_IaPc = iPr_def_10,
inference(demodulation,[status(thm)],[c_2139,c_436]) ).
tcf(c_2154,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_303,c_2142]) ).
tcf(c_2155,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 07:42:14 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.33 Running first-order theorem proving
% 0.03/0.33 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 2.88/0.99 % SZS status Started for theBenchmark.p
% 2.88/0.99 % SZS status Unsatisfiable for theBenchmark.p
% 2.88/0.99
% 2.88/0.99 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.88/0.99
% 2.88/0.99 % ------ iProver source info
% 2.88/0.99
% 2.88/0.99 % git: date: 2026-07-19 20:42:38 +0200
% 2.88/0.99 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.88/0.99 % git: non_committed_changes: false
% 2.88/0.99
% 2.88/0.99 % ------ Parsing...% successful
% 2.88/0.99
% 2.88/0.99
% 2.88/0.99 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.88/0.99
% 2.88/0.99 % ------ Preprocessing... sup_sim: 15 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.88/0.99
% 2.88/0.99 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.88/0.99 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.88/0.99
% 2.88/0.99 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.88/0.99 % ------ Proving...
% 2.88/0.99 % ------ Problem Properties
% 2.88/0.99
% 2.88/0.99 %
% 2.88/0.99 % clauses 14
% 2.88/0.99 % conjectures 0
% 2.88/0.99 % EPR 1
% 2.88/0.99 % Horn 14
% 2.88/0.99 % unary 14
% 2.88/0.99 % binary 0
% 2.88/0.99 % lits 14
% 2.88/0.99 % lits eq 14
% 2.88/0.99 % fd_pure 0
% 2.88/0.99 % fd_pseudo 0
% 2.88/0.99 % fd_cond 0
% 2.88/0.99 % fd_pseudo_cond 0
% 2.88/0.99 % AC symbols 1
% 2.88/0.99
% 2.88/0.99 % ------ Schedule UEQ
% 2.88/0.99
% 2.88/0.99 % ------ Option_UEQ Time Limit: 10.
% 2.88/0.99
% 2.88/0.99
% 2.88/0.99 % ------
% 2.88/0.99 % Current options:
% 2.88/0.99 % ------
% 2.88/0.99
% 2.88/0.99
% 2.88/0.99 %
% 2.88/0.99
% 2.88/0.99 % ------ Proving...
% 2.88/0.99 %
% 2.88/0.99
% 2.88/0.99 % SZS status Unsatisfiable for theBenchmark.p
% 2.88/0.99
% 2.88/0.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.88/0.99
% 2.88/0.99
%------------------------------------------------------------------------------